It's possible to deterministically sample from a probability distribution. For example, just seed your RNG with a constant, or with the SHA256 hash of the context.
Not really, LLMs give you a distribution over possible next tokens. You are free to then sample from this distribution how you want. There is no need to hack RNG or whatever, for example you can simply just take a greedy approach and always output the most likely token, in which case the LLM becomes deterministic (mathematically). This is equivalent to setting the temperature to 0.