awww...what fun is it if you hold us to the original question?

Ok, then...there are several more specific types under that general heading.

The most common is rhetorical questions, but this implies a question for which no answer is really expected...or in which the answer is already presumed.

Then there are 'questions' stated as puzzlements or bewilderments in which one can't find a simple answer....such as 'which came first, the chicken or the egg'? or "what is courage?" or...*shudder*
What is 'folk'?" These were called aporia in Greek.

Also. 'hypothetical' questions might be included..."What if we bred a platypus to an aardvark?" One can speculate as to features, but it can't actually be done..

I suppose some questions could be 'tautologies' in disguise...asking something that is self-referential by using two words that imply the same thing.

If you want to pursue other possibilites, this page on "rhetorical devices" lists a number of technical terms which 'could' be used to frame a question in some circumstances.