In modern English, we usually say "what" instead of "which," even when it really should be "which." Swedish stays true to that. It's vilken because you are asking which of the many possible origins "it" came from. It's kind of confusing, but you'll get used to it eventually.
You say "usually". This is why "Which is its origin?" was marked as wrong or would that be totally unacceptable in modern English (I know, it is an English question instead of a Swedish one, sorry if it feels off topic).
You could say "Which is its origin?" but in my opinion, it has a connotation that you are asking "Which (out of these choices) is its origin." In English, we tend to replace "which" (still preserved in many other languages) with "what" if you are not having to choose from certain choices. This is only my perception, so it may not be 100% correct, but I hope it helps!
I've added which as an accepted answer in English since I think that works too. As Super-Svensk says, it has the connotation of 'which one of the options', but so can vilket.
A short explanation about the "dess" word, please? I don't think I have seen it before in the course.