pronouns - Misunderstanding the use of me/him/her/them/us

I'm aware that when the pronoun is also the object of a sentence we use these: me instead of I, them instead of they and so on.

But when I say:

He is a teacher, and her?

Why do I say her instead of she if in this case I cannot identify a direct object.

Also when answering, would I say

Her, she is also a teacher.

or

She, she is also a teacher.

I'm really confused