This sentence is probably not legal. The object of Hon is supposed to be the thing doubted, but here you're trying to doubt a question, not an action.
lugh lurveng 'e' vIHon I doubt that Lurveng is right would be a valid sentence, but not if the first sentence is a question.
There's no definitive canon to back this up, and I'm not trying to completely disallow questions as objects (there is canon of such), but it follows from the given grammatical rules that the 'e' should refer to the thing actually doubted, not to your question of whether the thing you doubt is true.
The question word nuq goes into the sentence where the answer would be. The question is, What do you want to drink? If the answer is bloodwine, then the answer would be in Klingon, 'Iw HIq vItlhutlh vIneH. Now substitute in the question word and re-evaluate the prefixes: nuq Datlhutlh DaneH.
I was thinking for a couple minutes that it made sense but I am back to thinking it doesn't. It would say then, you want that you drink what or you want that what are you drinking. It still doesn't really make sense to me once nuq replaces the actual thing being drunk.
I don't think I am explaining myself very well but I don't see how DaneH can refer to the question of what you are drinking and have it make sense. It seems like the same problem with the sentence with lugh'a'.
I understand the problem you're seeing. Try to think of this as one whole sentence, nuq Datlhutlh DaneH, not as two separate sentences, nuq Datlhutlh and DaneH. You're taking the entire answer, 'Iw HIq vItlhutlh vIneH and turning it into a question by substituting nuq, which is always exactly what nuq does.
It may not be grammatical in every possible way of analyzing the sentence, but it's grammatical in one way, and that may be enough.
Who knows? Maybe it's one of those turns of phrase that has made it into mainstream Klingon culture (enough that they teach it to the tourists without comment), but stodgy Klingon grammarians turn their noses up at it as obviously wrong and uncouth.
Ah, yes. Ok. I can accept that. (My brain can absorb that without rejecting it like a splinter I mean.) I was wondering if maybe nuq could apply to the entire rest of the sentence.
Or maybe the other idea makes sense as well that it could be sort of a frozen expression such as "I could care less" which is commonly said in my region of America.
No; it's two sentences in Klingon.
Even lugh lurveng 'e' vIHon "I doubt that Lurveng is right" is technically two sentences in Klingon, even though we usually don't put any punctuation between them -- the first sentence is lugh lurveng and the second one is 'e' vIHon, where the special pronoun 'e' refers to the entire previous sentence.