1. What did you do with a student who was behind?
Not "how would you" — what did you actually do. A tutor with real experience has a specific story and a specific outcome.
2. How will I know it is working?
A good answer names something you can see in four weeks: a weekly test, a marked exercise book, a topic list that shortens.
3. What do you need from us?
A quiet room, a fixed hour, someone checking that the homework got done. A tutor who needs nothing from the household is usually a tutor who has not thought about it.
4. What happens if a class is missed?
Agree this before it happens, not the first time it does.
5. When would you tell us to stop?
The best answer is an honest one. A tutor willing to say "if there is no progress by the exams, you should try someone else" is a tutor confident enough to be worth keeping.