Okay, Vishnu, part of the trinity of classic Vedanta Hinduism, had over a dozen incarnations as humans, the two significant ones of which are as Krishna and Rama. Some Hindu-Buddhist syncretes claim that Siddhartha Gautama of the Sakyamuni clan was also an incarnation of Vishnu. There’s supposed to be one final incarnation of Vishnu, IIRC named Maitreya. AFAIK, Brahma and Siva never incarnated according to Hindu doctrine.
Baha’i considers that all the major religion-founders down to and including Mohammed were “mirrors” whereby their followers could see God – Baha’ullah being the last such “mirror.”
Christianity, of course, insists that there is only one true God, and that only the Second Person of it incarnated, and that only once, in the person of Jesus of Nazareth.
Islam is horrified at the idea that Allah the Merciful, above and distinct from His creation, might be thought to have ever entered into it to live as one of us. I believe that Judaism feels much the same way.
With regard to the OP:
Nope. He knows all from an eternal (not time-limited) perspective and is everywhere present at once.
Well, that depends on what you mean by “the rest of the universe.” It can be shown that the characteristics ascribed to God correspond to those required by taking the Lorenz transfer equations to a limit of infinity, hence those of a superluminal particle moving at infinite speed within a closed universe.
Hence if God interacts with His (physical) universe through physical form (other than in the capacity of Jesus the Incarnate Son, grist for a separate debate), He does it through such particles. And the reason why God “cannot be proven” through physical-science means is that we cannot detect superluminal particles (Cherenkov radiation, representing a very specialized exception to that rule, to one side).
“Before the Big Bang” is like “below absolute zero” or “north of the North Pole” – a verbalizable concept corresponding to nothing legitimate in the physical universe.
Yes and no. No, not necessarily – He created them along with the universe which they describe, and can alter them if He sees fit. Yes, IMHO – by self-limitation. He will “play by the rules” He made.