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.
or French ' poser des questions'
Samma sak på italienska:
"Porre una domanda".
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.
"My son keeps asking new questions." Seems to me just as idiomatic.
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?
Thinking about it i'd have to agree. The present continuous with "always" in English is a very natural way of phrasing something that would be in present tense with "ständigt" in Swedish.
How is "My son keeps asking new questions" not correct??