8. INTERSECTS always superior to ANDEQUALS and WITHIN 0 WORDS for typical usage scenarios? (Logos 7.1)
ANDEQUALS: Originally developed for English+Strongs (now English+lemma or lemma+morph) searching. Requires hits for the two terms to be exactly at the same offset and length. De-duplicates hits before returning them.
WITHIN 0 CHARS: Requires the two terms to be indexed at positions that differ by at most zero characters; in practice, this means intersection of hits. Returns all the hits without de-duplicating them.
WITHIN 0 WORDS: Should be the same as WITHIN 0 CHARS (except measured in words) except it looks like I found a bug that returns false positives (when word counts aren't known, e.g., for terms inside footnotes which don't count as words in the surface text?).
INTERSECTS: Requires the terms to have hits that intersect/overlap. Returns a new hit from just the overlapping portions of the hits and de-duplicates the results.
ANDEQUALS will remain the most "precise" operator (and should return a subset of the results from the other operators). All the operators can have false positives (for lemma@morph) when lemmas & morphs from two different Greek/Hebrew words are aligned to the same English word. ANDEQUALS can have false negatives (for English+lemma) when Greek/Hebrew is aligned to a phrase; the other operators can have false positives in that situation instead.
ANDEQUALS and INTERSECTS will probably return the result count you're expecting, i.e., the number of hits will be the number of distinct highlights shown in search results.
WITHIN 0 CHARS may still have some use for making matches from idioms more obvious because it will highlight the entirety of the matched idiom (e.g., "was the Lord's doing"), not just the smallest individual piece ("Lord" or "doing").
Probably a good rule of thumb is to always start with INTERSECTS by default, then consider switching to another operator if you're not getting the results you want, and if you understand why a different operator will give you different results?
Can we think of INTERSECTS as replacing these two operators for all practical purposes?
I think so, yes.
This being said, I am not sure I follow the reference to an idiomatic expression in the ESV as an explanation for the missing result when using ANDEQUALS: the surface text is what is being looked for by 'Lord' isn't it? And the underlying lemma certainly is kyrios. So I don't get why it's not a hit.
Here's an image that can help understand why ANDEQUALS comes up short in this particular case:

The text in the ESV interlinear is in italics, indicating this is an idiomatic expression. For idiomatic expressions, words have not been lined up one by one, but as a group.
With ANDEQUALS, things are supposed to start and end at the same "location". This almost always occurs with lemmas. But with these idiomatic phrases, the tagging doesn't define which lemma corresponds to which word in the idiomatic phrase. So, even though they "intersect", they don't start and end at the same location, so ANDEQUALS doesn't find them.
So, INTERSECTS gives more hits, normally correct hits. It might occasionally give a false positive. So:
lemma:κύριος INTERSECTS doing
returns Matthew 21:42, because doing is also part of the idiomatic expression.
But when we actually run real-life searches for words being translated, it's very hard for me to imagine a case where a false positive would occur with INTERSECTS (nobody searches for lemma:κύριος INTERSECTS doing in real life). It's much easier, I think, that you would miss hits with ANDEQUALS where you have idiomatic expressions, as in fact occurs in lemma:κύριος ANDEQUALS Lord.
. . .
The screenshot above from the Interlinear shows that the entire English phrase is tagged to the entire Greek phrase. But the specific English words are not aligned to specific Greek words. If they happen to be in the "right order", it is pure coincidence. That is why they are all blue. To select one is to select all three.
This is also reflected when right clicking on the word "Lord's":

The word "Lord's" is tagged to all three Greek words. Verbum has no idea which of the three it actually corresponds to in the ESV. (Note this doesn't apply to the original Greek versions, where each word is individually tagged).
The ANDEQUALS search that reflects what the Interlinear displays in the ESV would be this one, which returns Mt 21:42:
"παρὰ κυρίου ἐγένετο" ANDEQUALS "was the Lord’s doing"
ANDEQUALS doesn't work here because of what Bradley described as: "Requires hits for the two terms to be exactly at the same offset and length."
9. Which animals are listed in the Gospels?
Today for one reason or another the topic came up at lunch of what types of animals are named in the Gospels. We had a good time trying to think of as many as we could. Afterwards, I thought I would try finding the answer with Verbum 6, and I must say, it was quite easy. 
Here are the steps:
1. In the Bible search tab, limit your search to the "Gospels". Then type "animal". From the dropdown, select the "sense" animal.

Run the search. This will search for the sense of "animal" and also all subsenses, which include all the specific animals! (BTW, if you want to search for ONLY the sense "animal" without the subsenses, you can do so adding the equals sign, <Sense = animal>).

Now is where it gets really good. What if I actually want a list of all the animals? Verbum 6 can do that very easily as well. Just select "Save as Word List" from the dropdown.

Sort the list by "Gloss" if you like.

Note that apparently there is an error in the results! The results include "courtyard; palace", which is obviously not an animal!!
To figure out why this is the case, go back to your search panel, and switch over to the Analysis View. Then organize by Lemma and look for the corresponding lemma, αὐλή.

It is from John 10:1. If we look at the Reverse Interlinear data, we can see what is happening.

The whole phrase "dwelling of the sheep" is being translated with one word, "sheepfold", so that when we run the search on the English translation for <Sense animal>, all three Greek words are being returned.
It is easy to fix this, however, if you remember that all of the basic tagging is done on the Greek text of the SBLGNT. So, let's run the search over on the SBLGNT.

Notice that there are the same number of verse results, 152, but now we have 188 hits instead of 203. So, that means we have "shed" 15 false hits that were caused by the way the English translation translated the Greek words, as in the case of "sheepfold" translating "dwelling of the sheep".
Now, rerun the Save as Word List.

Now everything works correctly, with no false hits. You can then select Print/Export and export the list to Excel if you like.
Now, admittedly, having a complete and accurate list of what animals appear in the Gospels is probably not too useful for most people! But hopefully the principles illustrated can be useful - how <Sense> searches can search subsenses, the ability to create Word lists from searches, and how the SBLGNT is your go-to text when you need to make sure the tagging is correct.
how about an LN numbers search?
Better with simply <ln 4> - interestingly this gives almost the same results, with 204 hits in 153 verses in the RSV, that is, one more hit and one more verse. But, there is at least one very debatable hit, which is visible in your image there, Lk 9:42, not present in the <Sense animal> hits.
If you wanted to do a detailed comparison of which verse are returned by LN vs. which verses are returned by <Sense>, you could use this method here.
10. Why didn't Jesus choose a full-fledged Hebrew name for Peter?
Here are three methods that can be helpful in cases like this:
- Run an Exegetical Guide on John 1:42, and use the Lemma in Passage section to find commentaries in your library that discuss the lemma Κηφᾶς in John 1:42.
- Run a Bible Word Study on Κηφᾶς, and look in your Lexicons and Theological Dictionaries. Particularly helpful for more in depth studies are resources like the Theological Dictionary of the New Testament (which includes an article on Κηφᾶς). Also look at the Lemma in Passage section in the Bible Word Study, to get discussions from all your commentaries, even when not discussing John 1:42.
- On the Basic Search tab, search all resources using WITHIN {Milestone}. Then, organize your results By Count to easily see which commentaries are most relevant. For what you want, try something like:
[quote](syriac, aramaic, Kepha, Qepha, Cephas, Κηφᾶς) WITHIN {Milestone <John 1:42>}
Here are the books in my library with more than 5 hits:

Here are three methods that can be helpful in cases like this:
- Run an Exegetical Guide on John 1:42, and use the Lemma in Passage section to find commentaries in your library that discuss the lemma Κηφᾶς in John 1:42.
- Run a Bible Word Study on Κηφᾶς, and look in your Lexicons and Theological Dictionaries. Particularly helpful for more in depth studies are resources like the Theological Dictionary of the New Testament (which includes an article on Κηφᾶς). Also look at the Lemma in Passage section in the Bible Word Study, to get discussions from all your commentaries, even when not discussing John 1:42.
- On the Basic Search tab, search all resources using WITHIN {Milestone}. Then, organize your results By Count to easily see which commentaries are most relevant. For what you want, try something like:
[quote](syriac, aramaic, Kepha, Qepha, Cephas, Κηφᾶς) WITHIN {Milestone <John 1:42>}
Here are the books in my library with more than 5 hits:

If you or anyone else is interested in what languages Jesus, his disciples, and 1st century Judeans would have spoken, you will want to check out some of the contributions from Randall Buth and R. Steven Notley's rather hefty tome The Language Environment of First-Century Judaea (also see this suggestion thread). Sometimes scholars get their apples carts shaken and even turned over! Anyway, there should be plenty to consider. Here's a selection you can find online:
- Buth, Randall. “Differentiating Hebrew and Aramaic Backgrounds in Greek Writings.” Pages 247–319 in The Language Environment of First-Century Judaea. Vol. 2. Jerusalem Studies in the Synoptic Gospels. Leiden: Brill, 2014. Online: http://www.biblicallanguagecenter.com/language-background-literary-function-cry-cross/.
- ———. “Introduction: Language Issues Are Important for Gospel Studies.” Pages 1–5 in The Language Environment of First-Century Judaea. Vol. 2. Jerusalem Studies in the Synoptic Gospels. Leiden: Brill, 2014. Online: http://www.biblicallanguagecenter.com/volume-century-language-land-israel/.
- ———. “The Riddle of Jesus’ Cry from the Cross: The Meaning of Ηλι Ηλι Λαμα Σαβαχθανι (Matthew 27:46) and the Literary Function of Ελωι Ελωι Λειμα Σαβαχθανι (Mark 15:34).” Pages 395–421 in The Language Environment of First-Century Judaea. Vol. 2. Jerusalem Studies in the Synoptic Gospels. Leiden: Brill, 2014. Online: http://www.biblicallanguagecenter.com/language-background-literary-function-cry-cross/.
- Buth, Randall, and R. Steven Notley. The Language Environment of First-Century Judaea. Vol. 2. Jerusalem Studies in the Synoptic Gospels. Leiden: Brill, 2014. No pages. Online: http://www.biblicallanguagecenter.com/volume-century-language-land-israel/.
- Buth, Randall, and Chad Pierce. “Hebraisti in Ancient Texts: Does Ἑβραϊστί Ever Mean ‘Aramaic’?” Pages 66–109 in The Language Environment of First-Century Judaea. Vol. 2. Jerusalem Studies in the Synoptic Gospels. Leiden: Brill, 2014. Online: http://www.biblicallanguagecenter.com/hebraisti/.
- Fassberg, Steven E. “Which Semitic Language Did Jesus and Other Contemporary Jews Speak?” The Catholic Biblical Quarterly 74 (2012): 263–80.
11. find out what prophet's served during the reign of Uzziah of Judah
Yes, Fr. Devin was involved but is not quoted. The post is a good reminder that a search is not always the answer.
I don't think Clause Search is the right tool to figure this out. As its name implies, Clause Search finds related things that are mentioned in the same clause. Unless a biblical verse happens to mention a particular prophet in the same clause as Uzziah, Clause Search won't return it.
A better way to approach this may be to open Timeline, press Ctrl+F and type in Uzziah. When you find "Reign of Uzziah in Judah", hold down Shift and click that timeline event. The timeline will zoom to that event.
Now, in the Filter textbox, type: Uzziah OR prophet
The timeline will filter down to show any events that mention "Uzziah" (this keeps his reign visible) or contain the word "prophet". This should give a quick overview of the prophets who were active at the same time.

12. Making the most of Biblical People Diagrams
So Fr. Devin's involvement was appreciation but I did say "and friends"
I am sure that what I post here will be old news to many, but I thought it may be useful to others.
How to make the best of Biblical Persons Diagrams is not necessarily evident.
First, the way to access Biblical Persons Diagrams is not evident. The reason for this is that though it looks like a tool (and so one might think to look for it there), but it is in fact a resource. You may instinctively look for it among interactive media (after all, both the graphics and the icon look like those of interactive media) but will not find it there. The way to find it is just like a regular book in the library.

Second, Biblical Persons Diagrams contents are arranged by titles alphabetically, not by references. References are indicated in parentheses after the title, but there is no quick way of finding your passage else than by scrolling through the whole collection.

The turning point is realizing that this is a resource (a book) and thus, you can search it as you would a book. For instance, you can search for <Person name>. It will come up if you search Everything but it is more streamlined if the book is opened first from the library and then you select it in "search in" or you type the title in the search in box directly. You can also search for it under media search but really a basic search works just fine. In fact, I found that a media search only displays small previews whereas as you see in the example below, a basic search produces the charts titles as well.

I picked an easy example above (Abraham). But it can be a bit more complicated when you are searching for a person who is not the only one by that name. See for instance, Caleb:

Using * as a wildcard does not work. In this case, it is best to let the drop down list populate and choose the correct entry:


The other way of doing something like this is from a diagram, right-click on a person and search "this resource":

The other quite useful entry point is to search by <Bible reference>. [UPDATE: As MJ points out below, you can just do < reference >. This way, you can start from where you may be reading: Genesis, Chronicles, Nehemiah, etc:

13. Obsolete due to interactive Text Converter: how to use www.transliterate.com
I noticed that the www.transliterate.com website only outputs SBL format, not the Scientific format, so I tried again with the Lexham Hebrew-English Interlinear and finally figured out how to copy and paste with left to right text correctly formatted. Here are the steps:
- Select Tools – Program Settings
- Change the Hebrew Transliteration format to “Scientific”
- Open the Lexham Hebrew-English Interlinear Bible
- Click on the “display” button. Select “Inline”. Select “Manuscript (Transliterated)” and then deselect all the other options except these two. You will then see the Hebrew text transliterated according to the “Scientific” format.
- Select the text you want and copy it.
- Paste it into Word. Word has multiple ways it can paste a text, and each way will give you different results:
- Merge formatting – Will display the transliterated text from left to right (this is the option generally desired)
- Keep Source Formatting – Will display the transliterated text from right to left (this is what I see by default, and what others in this thread have mentioned they see)
- Keep Text Only – Will display the Hebrew text with Hebrew characters
It works great! Congrats to Logos for allowing so many ways to paste, and for hiding this fantastic feature so well! 
He also found this useful Link Zotero to a Logos Book
14. Root in Bible Word Study
This tip is very simple, but I find myself using it all the time now, so I thought I would share it.
Create a new Bible Word Study and add only the "Root" tool. I named it "BWS - Root".
Now, when you right click on a word and select Lemma, you can very quickly do a "Root" study, with no need to scroll down to the Root tool. This is extremely useful to get a feel for the semantic range of a word.
Here is an example of how this looks (although in this example I am right clicking on a Hebrew word, it works right clicking on a word in the Reverse Interlinear English Bibles as well):

Now the "BWS - Root" Bible Word Study opens right to the Root tool, with no need to scroll to compare all the roots and get a better feel for the semantic range of the word, learn new vocabulary, etc.

Now we just need Logos to allow us to "Send hyperlinks here" for Bible Word Studies, so that a new tab isn't opened each time a BWS is opened.