They can all be correct. It just depends on the rest of the sentence. I have already done the laundry, but I haven't folded and put it away yet. I already did my homework, so now I'm going out. I already do yoga every day, so I don't need more exercise.

You can use all of them in a sentence. They are all correct, if you use them in the right way.

The correct is I have already done.

As far as I know... In British English the correct is: “I have already done this....”, as you need to use Present Perfect (action in the past, which has an effect on the present) However, in American English “I did .... already” is correct as well.

i have already done and i already did