Unless you have something exotic, the randomness that's adding to a computer is a combination of how it's configured combined with a pseudo-random number generator. I assume the system adds entropy to the generator regularly but all you need to do is fix the various supposedly random inputs and you can get full determinism even without zero temperature.

Yes, in theory, of course.

In practice - on a multitasking OS with input from multiple human users - it's hard to get it deterministic because of that GPU scheduling thing I mentioned.