That's a tough question. As an english speaker I have never heard anyone say "of the question" However I don't think it is incorrect. Just it would be odd to say it and no native speakers would ever use it.

For both "answer" and "solution", it is ALWAYS "to" the problem. Here's the key: "of" means something is a part of or a product of the subject. We do not consider "solutions/answers" a PRODUCT of problems. Instead, solutions are a PRODUCT of the people who think them up in order TO address the problem. "to" means it is directed at the subject, or a corresponding part TO the subject. There is a difference between a part OF something, and *the* corresponding part TO something. Let's look at some examples: "This is the key to the lock." "This is part of the lock." The word "lock" is defined as all the bits and pieces that go together to do the locking. It absolutely DOES NOT include the key. It is everything BUT the key. Contrast this with: "This is a piece of the puzzle." A "puzzle" is DEFINED as the entire collection of all the pieces. Now here's a tricky one: "This is the last piece TO that puzzle." Why on earth is it "to" now!? Well that is because the scenario is like this: You leave an incomplete puzzle on the table and go looking for the last piece. When you find it, you are essentially saying: "This is the missing piece! It is the last piece to that INCOMPLETE puzzle!" In your mind, the puzzle has changed from something possessing all the pieces, to something irritatingly missing one piece. It has turned into a lock, and you are looking for the final key. That is why you might see "piece TO the puzzle" sometimes, but if you are trying to be as correct as possible, "...the last piece OF the puzzle..." is better. There are many other tricky cases of "of" versus "to": He is the subject of much talk. He is subject to much abuse. He was a slave of a Roman aristocrat. He was a slave to his drinking habits. It poses a threat to him. Under threat of death. Adviser to the king. Subject of the king.

I would not say "the answer of the question" because it sounds like "the answer" is an innate part of the question. I would also say "the solution to this problem" for the same reason. An answer is not essential for a question to exist or be a question. You would typically say "the solution to the problem" unless 1. you are very specifically talking about a problem that you are currently facing, or 2. you have some sort of list of problems (like math problems) in front of you, and you have the solution to a specific one on the list.

Probably is correct, but this not sounds natural.