A short disclaimer before answering. Right now I'm doing a Mathematics & Physics undergrad degree and have interest in philosophy. I'm not a specialist in any of those fields. I have plans to tackle the actual math around LLM's a bit further, but I'm not there yet.

To question 1 based on my current understanding (and let's say "beliefs") is that - yes, LLM's are following a probabilistic algorithm to give me the output. The same prompt won't yield the same result, but the same prompt will yield results that are quite adjacent to each other in meaning because of the training. There's randomness in the sense that you can't say which next token will be put with certainty, BUT you can be certain it will be a token that exists in the pool of tokens available. Hopefully that makes sense?

For question 2. Both us and LLMs are constrained by physics. The main difference for me is the fact that at every point of our existence we're constantly changing. Our internal state and bodies are changing based on all the sensory input we get from our environment and the processes that lie underneath. Another commenter in this thread talked about qualia. That's certainly part of it as well (but again we have a definition problem). That's not to say that I think that a hypothetical future machine cannot be devised to handle a lot of these, but the level of sophistication in the biological world is such that I don't think that's realistic. Let's say that even then, that happens, would that really prove that humans work the same way as the machine?

I would be interested in the answer to this question too. The visual cortex is certainly algorithmic in that light data enters, various cells and synapses react and fire and that information is ingested into something 'conscious'. Where does this then exist, and would it even be able to exist if we removed the biological algorithms at play?