Yes, you can say that, it is correct. Examples: Did you finish your homework? Yes, I'm done! Are you finished eating? No, I'm not done yet! I'm done with the bathroom cleaning. When I'm done with this project, I'm going to take a break. Sorry, are you done with this? Yes, I'm done!

You are correct. Saying I'm done, means you have finished something

"I'm done" is often used in that context. In the US another very common expression with the same meaning is, "I'm through." BTW, we would say, "Once I finished DOING sth..."

Sure you can! And it also seems more natural into the english context of language.