For number one, you're using 'done' to mean finished. Therefore, the correct sentence is I'm done talking with her. The second sentence is not grammatically correct but you could say 'I have finished talking with her'. There is a slight difference in meaning though. The first sentence, with 'done' could be used when you're angry or upset and no longer want to talk to someone. The second set has the same problem with I am done eating being the correct option. In the third set, I have finished my homework is the normal option in British English whereas I finished my homework is perhaps more normal in American English. Often, past simple (the structure you have in the second sentence here) is used with a specific time in British English.

You cannot say I have done talking with her. Done doesn't express the idea you finished something. So if you add the verb of to be then "done" will express the idea you finished something. I am done talking with her is correct 👍🏻

The word [done] should not be used in good writing to mean finished or completed. It is proper to say “the roast is done,” but this does not mean it is finished; it means the roast is sufficiently cooked. —Theodore Bernstein, The Careful Writer, 1965 The “food is done” line has been a very successful one, and still appears occasionally today. When you have finished eating, please don’t say that you are done. People are “finished.” Cakes are “done.” —Lydia Ramsey, Dottie Walters, Manners that Sell: Adding the Polish that Builds Profits, 2008 For more explanation check : merriam-webster

In my view, i can say something for your sentences. 1) In grammar rules: we must use, I have done talking with her. 2) I have done eating, seems okay. ("have" indicated "just now" expression. Also, you can use i finished my lunch. ) 3) I have finished my homework.(just now) and "I finished my homework." are correct. (But the first sentence has a mistake about grammar rule.