"Do you hate each other?"
Translation:Siz birbirinizden nefret mi ediyorsunuz?
Expanding on deorme's comment:
"[…] Nefret ediyor musunuz?" would mean you're questioning the entire "hating". And that would be used when you naturally expected this to happen. For example, lately you have seen many couples who hate each other, and now you have met a new couple and ask them: "So, do you hate each other? - No, I'm just asking, because apparently it's become the norm by now, but if you don't want to answer, that's fine."
"[…] Nefret mi ediyorsunuz?" is harder to see in English, but it's more apparent in Turkish, because "nefret etmek" is a phrasal verb. "Etmek" is used with hundred thousand other words to give different meanings, kind of like "up" in English (take up, sit up, shut up, knock up…). So the idea here is, you're saying: "I know that you "etmek" a lot of things to each other. There are a hundred thousand behaviours that we express with 'etmek' that are valid for you. But "nefret"??? Is that one of them too? Jesus! Do you really HATE each other?"
Not sure how much more sense this has made, but I thought I'd share my point of view.