1)Yes,he is.He is going to the library.
2)No,they aren't.They are having a rest.
3)Yes,I am.I am having visitors.
4)No,she isn't.She is staying at home.
5)No,they aren't.They are having a holiday.
6)Yes,he is.He is going to the concert.
7)Yes,I am.I am having an English class.