Do you know her?
-Is she the actress who always plays bizarre characters?
-Yes, that's her. Shall I introduce you?
-That would be fabulous. I'm going to ask for her autograph.
(Would you check the dialogue? Are the sentences all grammatical? Would you correct errors?)
They are all fine for everyday conversation.
Technically, it should be "that's she" because you need the subject form of the pronoun. However, you'd only need to be that correct in formal papers.
Most English speakers say "that's her." Languages are constantly changing and I think that's one usage that is in the process of changing.
The dialogue you provided is mostly grammatically correct. However, there are a few changes I would suggest to make it sound more natural:
"Do you know her?"
- "Is she the actress who always plays bizarre characters?"
- "Yes, that's her. Should I introduce you?"
- "That would be fabulous. I'm going to ask for her autograph."
In the revised version, I changed "Shall I introduce you?" to "Should I introduce you?" This change makes the question sound more conversational. Additionally, I removed the hyphen separating the first and second lines, as it is not necessary in this context.