Why is "kim kahveyi yaptı" wrong?
it is not wrong but it is very strange. if you ask who did something, the emphasis is on "WHO"; which means it (kim) should come before the verb. Your sentence puts stress on "kahveyi"
So this might be used if someone said "Selcen made the tea" - "OK, but who made the COFFEE?" I was thinking in terms of SOV word order, but I guess question words like "kim" or "ne" should always be right before the verb, right?
yes it could be used in such a situation. and yes often they come right before the verb
That was my question too, so teşekkurler
'kim kahveyi yaptı' was rejected - I will report it?
I had similar thoughts as brjaga. So, emphasis "beats" standard word order (if you can call it that).