both are fine, but provide different information in Turkish:
- "Siz birbirinizden nefret mi ediyorsunuz?": The person asking the question assumes that you hate each other, and asks this or confirmation.
- "Siz birbirinizden nefret ediyor musunuz?": The person asking the question has no idea if you hate each other or not.
Sorry there is ine point I'm missing here, isn't the "mi" indicating a question? Where is the negation here? And earlier in another discussion it was explained that the questioning "mi...etc" is only placed after the reflexive in these types of sentences. Can you clear this up?
That is fine and is already accepted, but I think you have some terminology mixed up.
What you used is a question particle, not negation. It is for forming yes/no questions and occurs after the tense information on the verb.
Negation (which looks similar) makes a verb negative (which is translated with "not" in English). This suffix comes before the tense information. So 'nefret ediyorsunuz" negated would be "nefret etmiyorsunuz." :)
In English, the adjectives "each" and "every" imply singular things and are always followed by a singular noun. For example, "Give each other a hug," "Every desk was made of wood," "Each voter is given a ballot."
Note that in other situations, the word "other" can be plural: "I liked this movie, but I liked others better," "John is going to the ball game now. The others are going later."