I was just wondering, how can we differentiate "are you done?" and "have you done?", and what is the appropriate way to use each?
"Are you done" asks about whether you have finished something that you have started. "Have you done" also asks if you have finished, but whether you have even started is uncertain.
("Are you done" can also be used in a "correcting" or "accusatory" way, where the asker knows full well you haven't started and that is the point he is trying to make. But that is not the normal case.)
When asking "Have you done?", you are asking if the person did something in the past which could continue to the present or have some implications to the present.
"Are you done?", on the other hand, actually means "have you finished?". That is, you are asking if the person completed the action started in the past (even though such action may also have implications to the present).
"Are you done" is used when asking a person if he or she has finished doing something. The thing that is being done is known.
Are you done with washing the toilet?
"Have you done" is asked when the thing being done is not known, and the person is inquiring as to what the thing is.
What exactly have you done to my car?
So, if you want to ask if someone has finished doing something, used "are you done?", or "have you finished?" , but not "have you done?"
Use "have you done" when asking about something that has happened, and you don't know. e.g. What have you done to him?