Is there any semantic difference between "Did you already" and "Have you already" questions?
For example:
1a) Did you already do your homework?
1b) Have you already done your homework?
2a) Did you already draw that picture?
2b) Have you already drawn that picture?
3a) Did you already clean my room?
3b) Have you already cleaned my room?
4a) Did you already return your debt?
4b) Have you already returned your debt?
5a) Did you already go to that café?
5b) Have you already gone to that café?
etc.
Remark: I am asking specifically about questions containing adverb "already".
Best Answer
With "already", they mean the same thing. The function implied by "already" is "a completed action in the past with present result". The difference between the two types is Americans tend to prefer the simple past version, while everyone else --including Canadians-- prefers the present perfect.
The only exception is with 5. "Go" has two different present perfect forms, each with its own meaning: "have you gone" means "have you left/departed", while "have you been" means "have you gone and come back". For example, "He has gone to the grocery store" means "He has left for the grocery store and not come back yet." Compare that with "He has been to the grocery store", which literally means "He has gone and returned from the grocery store", but most likely has the intent of, "He has done the grocery shopping."
So your question 5b) means, "Have you already left home for the café?" while your intended meaning was probably, "Have you already visited and experienced that café?", which is naturally expressed by, "Have you already been to that café?"
And to be clear, the word "already" doesn't change the grammar rules or meanings of simple past vs. present perfect. In this context all it does it make totally unambiguous what the intended function is.