Is ställer supposed to act like "poses" in this instance? Likewise, would this be the most common way of saying "asking a question"?
Yes. And yes.
We also sometimes talk about putting a question to someone in English.
Why not "frågar" in place of "ställer"?
You can say that and get away with it, but the most common verb used to ask a question is "ställa". It can be compared, as VikingPunkology proposed here in the comments, to the way you "pose a question" in English.
Can it be "presents new questions"?
It sounds to me like My son keeps asking new questions. Am I wrong? If I am, how this would translate to Swedish.
Why would "My son is always asking new questions" not be correct?
Always -> alltid?