1. mustn't (It is generally not allowed to walk on the grass in a park.)
2. mustn't (It's important for safety and politeness to not talk to the driver on a bus.)
3. may not/must not (Libraries usually have rules about borrowing, and 'may not' or 'must not' fits the context of permission being denied or a rule being enforced.)
4. must (In an exam, it is a requirement to answer all questions.)
5. must (Driving a car requires a licence, so it's a necessity.)
6. may (Guests have permission to use the pool during specified hours.)