Another useful one is to ask him to explain his reasoning.

If he can't justify his decisions, then he's probably using instinct which is unreliable in the case of rare diseases, or he doesn't know how to diagnose known diseases which means he's incompetent.

Some people are offended when you challenge them for reasons for their advice, but I think that's because they aren't confident in it themselves or feel superior. Doctors shouldn't be in either of those positions and should be willing to tell you how they came to their conclusions.

Whilst on the whole I agree with you, the amount of doctors I know that would react (quite strongly) negatively to that is quite high, so anyone who takes your advice should be prepared. The most common response I've seen to your question was the doctor reminding the patient "there is always something called a second opinion", a couple of times though I noticed them taking the time to explain it.

Why is "numbers per 10,000 people" meaningfully different than taking the percentage and multiplying it by 100?

Doctors and patients do not know what you mean when you say "your risk has gone up 50%". When you say "in a group of ten thousand people we would expect 4 to experience this thing. But in a group of 10,000 people who eat peas we expect about 6 people to experience this thing".

Gerd Gigerenzer has a book explainin it better than I do.