Not necessarily, GPU compute can be non-deterministic due to scheduling: the result of A+B+C is subtly different when it's (A+B)+C or when it's A+(B+C), which can get amplified in a long processing pipeline
Depends. The default script uses a non-deterministic stochastic encode for img2img. That would need to be modified as far as I know.
On the forked repo with the webui (https://github.com/hlky/stable-diffusion) it seems that the same inputs result in the same output, so maybe it has been resolved there?