"Have you calmed down?" is correct. "Are you calm down" isn't grammatically correct.It should be "Are you calmed down?". "to calm down" is a verb. "calmed down" is an adjective (the past participle form of "to calm down"). "Did you calm down" is correct. "Do you calm down" is incorrect. "Do you" (in the present tense) seems to be asking about a regular action or activity. Asking someone if they regularly "calm down" doesn't really make sense. You only calm down if you're fired up. You don't just randomly and regularly calm down. You have to start from a very specific state (upset, angry, agitated, etc). Asking someone "Do you dance" or "Do you eat meat" or something like that makes sense because those are things people do regularly that make sense. There are no special conditions to dance or eat meat. You can just do those things.

You can say "have you calmed down?" You can also say "are you calm?"