I would also like to know this. I think they're not interchangeable because in the question 'what is he wondering about?' I put 'hva undrer han seg på' and it was marked wrong, the correct answer was 'hva undrer han seg over'. So why was på wrong in that one? Is it because there was no specified object?
I am Norwegian and I would never say:: Jeg undrer meg på/jeg undrer meg over. I would say: "Jeg lurer på ....... If I were forced to use this expression and I had to choose I would use på instead of over. But you can just forget this problem, because if you go to Norway you could say: "Jeg lurer på hva det betyr."
Yes, people would laugh if you said 'undrer du deg på hva det betyr. ' There is a famous poem by Bjørnstjerne Bjørnson (1892 - 1910). It begins like this:
Undrer meg på hva jeg får at se over de høye fjelle ....
You find it, searching for this sentence or his name at Wikipedia.
Not really, you already have "do" at the beginning of the question you wouldn't need another form "does" later in the subordinate clause, unless you were quoting exactly what you wondered as in: Do you wonder, "What does it mean?" ? in which the quote is able to stand on its own.
"Do you wonder what it means?" was accepted as correct for me.