Usually we say “any questions” in the plural, but that’s only because we would expect there to be more than just one question. If, however, “question” means “doubt”, then yes, it would be common enough to use the singular. “Is there any question that Mandarin has more speakers than any other language?” (Answer: No, there is no question at all.) In fact, we can use “any” in the singular any time that we suspect the answer is singular: “Is there any reason that we should not proceed with our plans?” (The speaker expects that there is no reason, or at most one reason. Answer: “No, there isn’t any reason.” (= There is no reason.)

'Any questions ?' is correct. The odd time you will hear 'Any Question'. It's incorrect, but the speaker is being a little lazy and careless. Maybe he/she was thinking 'Do you have a question ?', but oped for 'Any question' because of speed and laziness. It's also possible they were think 'Any questions', but again dropped the 's' just to get it out faster.

If "any" means "none" or "does it exist", follow it with a plural. If it means "pick one", follow it with a singular. "Do you have any dogs?" 'no, we don't have any dogs, but you can take any cat that you want.' Here, the question is whether or not any questions exist, so use a plural and say "questions".

"Any questions?" is correct. If you want to use "question", you would ask "Do/Did you have a question?"