Dipok didn't quote Hawking, and didn't mention what particular program or interview they watched, and Hawking gave a lot of interviews, so there's no way to be sure what prompted this question. But Hawking famously wrote in A Brief History of Time:
The idea that space and time may form a closed surface without boundary also has profound implications for the role of God in the affairs of the universe. With the success of scientific theories in describing events, most people have come to believe that God allows the universe to evolve according to a set of laws and does not intervene in the universe to break these laws. However, the laws do not tell us what the universe should have looked like when it started—it would still be up to God to wind up the clockwork and choose how to start it off. So long as the universe had a beginning, we could suppose it had a creator. But if the universe is really completely self-contained, having no boundary or edge, it would have neither beginning nor end: it would simply be. What place, then, for a creator?
and he said similar things in interviews. Dipok's "God does not exist since the universe had an origin, and before it time and space did not exist; so it is impossible to create things in a timeless dimension" is probably a garbled version of that. I'm sure it's not what Hawking said, because the universe doesn't have an origin in his preferred model; that was the whole point.
The first-cause argument already looks a bit dicey in light of special and general relativity, according to which time is just another direction. One presumably wouldn't argue that God made one side of the universe and then let natural laws determine the rest, so why argue that God made the "bottom" of the universe, which is almost the same thing?
In Hawking's (nonstandard) "no-boundary" cosmological model, that problem is sharper, because the big bang is replaced by a gravitational instanton in which all four dimensions are on equal footing. There is no light-cone structure to give a meaning to "earlier" and "later" times, and there is no part of the instanton that is an uncaused causer of the rest of it. So his model is a counterexample to the assumptions of the first-cause argument, and since his model may be correct, the first-cause argument fails.
Good or bad, that was Hawking's argument. Dipok's question is founded on a misunderstanding of it, and all of the earlier answers seem to have taken Dipok's version at face value.
The answer to Dipok's question #1 ("Is Stephen Hawking assuming that God is an immanent entity?") is no. The other two questions seem to depend on the answer to the first one being yes.