Yes, these and the Hindus' Brahman, the Stoics' Zeus, and so on, are all just different names for the exact same being. By definition, there can be only one Ultimate Reality, even if people disagree on what he is like, or how to worship him, or how or even whether he interacts with his creation at all. For example, Christians and Jews have different conceptions of God, but that doesn't mean they don't believe in the same God. It's a basic category error to conflate God with a god. They're very different concepts.
Depends what you mean by proof. For those who accept reason, God's existence borders on the self-evident. However, if you deny that contingent being must have a ground for its existence, then naturally you won't be convinced of the existence of a non-contingent Ground of Being."for ultimate reality" again a non provable belief that you have to be honest about will not clear until we individually punch our ticket off the mortal coil.
No, read my post again. There's only one capital-g God; it's a proper noun, a name, that's why we capitalize it. There are potentially thousands or millions of small-g gods, but these deities are finite beings, belonging to an entirely different category of being than the Ultimate Reality, the ground of all being, which we name God.
Most polytheists easily grasp the difference between God and god. I recommend reading "God, gods and fairies", and chapters 4-10 of Athenagoras's "Plea for the Christians", addressed to the pagan Emperor Marcus Aurelius. They explain this quite well.
https://www.firstthings.com/article/...ds-and-fairies
http://www.newadvent.org/fathers/0205.htm