What are questions like
Why did the chicken cross the road?
called? I want to know if there is a particular term given to these type of questions.
Though this kind of question could be called a 'joke' - the humorous context of some questions can allude to a deeper philosophical proposition.... which can be funny in the context it is presented.
Consider the parable(s) of the Sphinx, and mythological creature that tested the dimensions of character through riddles.
I like the etymological root of "sphinx" ("shesepankh"), meaning "living image", because of the poetic connection to the life that is ultra-present in questions like are asked-about here (jokes, riddles, etc). I think these questions are 'more alive' and thus are more of a "living image"