Is there any way to limit clauses to a question (or not a question) in a Syntax search or using the Morph Query Editor?
Morph Query Editor is not a tool for Clauses.
In Syntax Search, there is nothing for NT Clauses, but you can query Interrogatives in Clause IC's (Andersen-Forbes). So you could ask for Clauses that contain Interrogatives, or do not contain them.
Otherwise, you can use datasets for text Searches. Go to Tools > Bible Browser and type Question. You can use Literary Types, Speech Acts, Propositional Outlines or the exclusive Questions dataset.