1) Hallucination rate is not inversely proportional to number of samples, unless you assume statistical independence. As you’re sampling from the same generative process each time, any inherent bias of the LLM could affect every sample (eg see golden gate Claude). Naively calculating hallucination rate as P^N is going to be a massive underestimate of the true error rate for many tasks requiring factual accuracy.
2) You’re right that output tokens are generated autoregressively, but you are thinking like a human. Transformer attention layers are permutation invariant. The ordering of output (eg decision first then justification later) is inconsequential, either can be derived from input context and hidden state where there is no causal masking of attention.