Is it possible that there are no answers to some questions, so the questions remain questions?

There can always be some kind of an answer -even if it seems not to make sense in order to start a debate then someone with imagination might come up with something interesting.

Yes there are questions that do not have answers. Humans tend to make an answer to tidy things up. We don't like unanswered questions.

Our imagination will create answers when we cannot find the real answer.

No, not in my life. 

i think its possible