Is there a way to copy a marked and highlighted text, keeping the markups?
Desktop? Mobile?
Desktop
Maybe. The markups that are compatible with Word options can be preserved in an export; incompatible markups will be dropped. If you'ver used many incompatible markups then a screen shot may be the best option.
Thinking outside the box, yes, if you don't care about editing the text. Screenshots of your marked up text will obviously preserve everything you can see. But you won't be able to edit the text.
[Edit: I said all that not knowing if there is software available that will read the text in the screen shots and re-convert it to text...so the last caveat may be correctable...I don't know.]
You can also print/export a selection of text to a PDF:
Yes, there are a number of such programs.
Sorry, I don't think I understood your question. You were asking if you can keep the markups when you PASTE it into another software program. Is that right? Others have given the basic answer: Only compatible markups will remain. If you have bolded, underlined or italicized text, that should remain. If you highlight text, that will probably not remain.
In Windows a number of the color features will also come across IIRC.
