I believe it is Nurture, if by Nurture you are referring to the programming and indoctrination of individuals from early childhood. Psychologists might consider the vicious cycle of a society which indoctrinates in this way as a form of a mental disorder. Not an expert on psychology, but if they do consider it, then I guess it is both.

In a big quote from Dawkins he uses megalomaniacal, sadomasochistic as a part of his description of the biblical god. So, yes, I think it is very likely.

Everything is a consequence of nature, but if it's science you go by, it doesn't classify belief of God as a mental disorder. Believing that 'belief in gods is a mental disorder' is as unscientific as believing in a literal god.

How about a mental disorder perpetuated since ever?

If someone were to start talking about Zuse, Hades or Poseidon we know this is classic mythology. When someone starts talking about the current deity or demigod my eyes roll that they can not see the delusions they are indulging in.

Yes