If I leave out the 'senin', how does this affect the sentence? Do we have to put a suffix behind ne in that case?
No, "senin" is optional. You don't change anything.
Senin adın ne? = Adın ne?
Neredesin = where are you
Nesin = what are you
Nerede = where is it
Ne = what is it
so if I am in a class and want to say "what are your names?" shall I say "Adlarınız ne?" ? Am I getting this right? Thanks for your reply and thanks for advance :)
Now, since it seems OK to ask, "Ne yapıyorsun?" would it be wrong to say "Ne senin adın?" or even "Ne o?" or "Kim o?"
No, ne senin adin equates to "what your is name" all correct words, but wrong order. That is what we call "a dusuk cumle" improper sentense, you get the message across though