Not sure about this "What are you doing this weekend" sounds more appropriate than "what do you do this weekend"
"This weekend" can also mean "next weekend" or "last weekend" depending on the tense of the sentence. Am I correct in assuming that it is not the case of "most hétvégén"?
No, it can mean this past weekend, as well, if you are saying something in the past. And next weekend only for this current week.
There are also two different uses in English depending where you are from. For me "next weekend" is the weekend after this coming weekend - ie two weeks away. Since I've moved I've insisted people give me dates!