So/ Neither with verb To Be and modals

[Anonymous]

Is it OK to say?:
1. Bill is a Peruvian. So am I.
2. They are in problems. So are we.
3. You aren't old. Neither are they.
4. Mary was in Egypt. So was she.
5. My father is a doctor. So is mine. (or So is my father). r both correct?
6. -I wouldn't do that.
-Neither would I.
7. They have gone to the USA. So have I.
8. She hasn't bought anything. Neither has he.

Thank you very much.

[Rusty]

1. Bill is a Peruvian. So am I. (OK).
2. They are in problems. So are we. (No).
(They are in trouble. So are we.
They have problems. So do we).
3. You aren't old. Neither are they. (OK).
4. Mary was in Egypt. So was she.
5. My father is a doctor. So is mine. (or So is my father). r both correct?(Yes).
6. -I wouldn't do that.
-Neither would I. (OK).
7. They have gone to the USA. So have I. (OK).
8. She hasn't bought anything. Neither has he. (OK).