I agree with Nicol Bolas, the questions you gave as example are too broad, I don't know where on this site game design related questions belong, but if you are too ask questions about game design anywhere, they would need to be very specific in order to inspire useful answers.
Also, a big part of the problem with questions related to game design is that the majority who ask questions about it seem to not understand what game design actually is. It has less to do with the "mood" of a game or "choosing soundtrack", and more to do with gameplay rules. Game design is very technical.
If an official definition of "game designer" existed I'd like it to be something along this, which I copied from Wikipedia: "A game designer is a person who designs gameplay, conceiving and designing the rules and structure of a game."
Since game design is of course a big (and crucial) part of any game development, and can be very technical, questions about it should actually be well-suited to gamedev.stack, but it's a subject that probably would need heavy moderation, more so than most topics asked about on gamedev.stack. On the other hand a lot of game design decisions has to do with which technology to use, and again, those questions are not allowed here (I learned that with my very first question).
It's difficult trying to come up with some random examples of what I think would be valid questions, as like I said earlier they would have to be very specific. But when talking about game design you can touch on a number of interesting subjects like game theory (no, not the theory of making games), chaos theory, algorithms, game complexity, emergence, decision trees, fuzzy state machines, etc, etc.