Difference between "are you done" and "have you done."

Solution 1:

"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.)

Solution 2:

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).