"Yine mi adaysın?"

They are the same, although "yine" is a little more common :)

this is not the regular word order for questions in English. Some of these sentences are shared with the reverse course, for people learning English so we stick to the grammatical word orders.

for the second one I would use "Aday yine sen misin?"

I am learning as well, therefore anybody should correct mi if I am wrong. I think "aday" is "candidate", means only the noun. For "to candidate" you should use "aday olmak".

yeni = new, yine = again