1) He said that I had to(must) try his home-made pie.
2) He asked me if he could go home then.
3) He asked her if he might call her by first name.
4) She told him that he could come in , but he didn`t have to make any noise.
5) She wondered what time they would arrive in London.
6) He admitted that she had to (must) try harder if she wanted to succeed.
7) She said that her father would be angry with her, if he found out.
8) He told her that she ought not to drive so fast или He advised her not to drive so fast.
9) He said that they didn't have to come if they didn't feel like it.
10) She advised him to speak to the manager.
11) He told her that he might not be able to meet her at the airport.