The correct answers for the given sentences are as follows:
1. He should cycle to school. It's cheaper than the bus.
Correct answer: (a) should
2. My dad has to start work at eight o'clock.
Correct answer: (a) has to
3. I must get up at six o'clock on Mondays. I hate Mondays!
Correct answer: (b) have to
4. You mustn't be late. It's rude.
Correct answer: (b) mustn't
5. We don't have to leave now. We can leave later.
Correct answer: (c) don't have to
6. You mustn't copy my homework! It isn't fair!
Correct answer: (a) mustn't
7. Marc doesn't have to do the washing-up. He's already done it three times this week.
Correct answer: (a) doesn't have to
These answers correspond to the modal verbs used in each sentence to express obligation, necessity, or permission. The modal verbs "should," "has to," "have to," "mustn't," "don't have to," and "doesn't have to" convey different meanings in terms of what is required or recommended in each situation.