Regarding your last question, ChatGPT isn’t deterministic. It can certainly give a correct answer one time and an incorrect answer another time, for the same prompt.
It's supposed to be deterministic if you set temperature to 0.0, but seems that doesn't work well in GPT4 compared to earlier versions...
That would be deal breaker if the same prompt gives different results.
Would also make the whole prompt engineering thing pretty useless.
There are also such comments on this article.