Yes and No answers

Hello, when we have "yes/no" answers, ca we shorten them regardless we use: is, are, was, were, do, does, or did?

For example can we say?
Q: Does she like coffee?
A: Yes, she does.

instead of:

A: Yes, she likes coffee.

I write more examples. Are all these correct?

Q: Did you buy carrots?
A: Yes, I did.

Q: Are you thirsty?
A: Yes, I am.

Q: Was you a doctor?
A: No, I was not.