What should one do when having a short question to which one can't find the answer? With short questions I mean question which generally can be answered with 'no' or 'yes', a simple example, a simple hint, so on and so forth. Are we allowed to ask such short questions or not?
Yes. $ $
Feel free to ask! Most questions on the site (not all mind you) have answers which aren't that long, only a few lines, and of these, almost all can have the main ideas of the answer summed up nicely with a short, one or two line hint (or a simple example/counterexample).
There's no problem with asking short/easy questions, although if there isn't much indication in the question that the asker has done any work towards the answer the most likely response is a comment saying "what have you tried" (and rightly so, in my opinion). Provided there is some form of working in the question, I can't imagine there are any objections that people could possibly have.
A good example of this type of question that has sprung up recently is the "check my proof" type questions, which provide a problem and a complete, or nearly complete proof where the actual question is just "is this proof correct?". Correct proofs usually get a comment saying something along the lines of "seems fine" and I've seen incorrect ones get quite good fixes for the given proof, and/or potentially better methods of doing it. No-one seems to mind these questions, and asking them appears to be very helpful.
Yes, you are most welcome to ask such questions. In general, don't worry too much about how you think the answer might be. If you have a legitimate question, then just ask.
Even though an answer might just be 'yes', the answerer might still be able to point out some background. In my limited experience, if a person asks a simple question that simple 'yes' or 'no' answer, the question usually reveals something deeper that the questioner might have missed or misunderstood. A good answer might also point out how something simple is actually part of a bigger theory.
"Can $a^n + b^n = c^n$ be satisfied for integers $a$, $b$, and $c$ for $n>2$?"
Conclusion: people do not study math to find terse answers to complex questions. I am hopeful that most answerers on this site will understand this and elaborate where it is warranted.