There is no hard rule on how many questions are too many. I'd like to change your perspective a bit here:
In general, focus on quality over quantity. Focus on the questions that enable you to derive value from the answer for your approach to the case.
You could ask 5 questions that are absolutely unrelated to the case prompt and client problem and won't help you come up with a proper issue tree. From my observations the more questions a candidate or coachee asks the more insecure they appear. They are fishing in the dark and appear a bit clueless.
Then, you could ask 1 or 2 killer questions that give you a lot of insights into the client's problem, thereby influencing your approach and shaping your hypotheses.
Summing up, try to focus on these killer questions that are
- relevant to the case
- based on common sense and an investigative mindset
- natural and not learned by heart like a framework to be used for every case