2 and 4 are incorrect and unnatural. 1 is correct and rebuts a suggestion that you still need to do the paperwork. 3 is ok. Also to be considered are: l’ve done the paperwork already. (The use of ‘already’ suggests that you aren’t interested in the past event but the present consequence of the past event.) The paperwork’s done. (More succinct if it’s obvious or unimportant who did it)

As others have said, 2 and 4 are incorrect. For formal English, I HAVE ALREADY DONE is preferred. English Grammar in Use by Murphy states that I HAVE DONE (present perfect) and I DID (past simple) are often interchangeable in informal English with British speakers tending to use I HAVE DONE and American speakers tending to use I DID.

I agree with DavidK. We use the verb 'do' instead of 'make' because we are not creating something new here. The word 'already' usually goes before the verb in English so 3 is the best option of the 4 options you give. However, the present perfect would also be better than the simple past because we are talking about a past action that has an effect on the present tense. Personally, I'd use 'I've already done the paperwork / I have already done the paperwork'.

It must be really interesting to get so many different answers to what seems to be a simple question, but the truth of the matter is the different people say different things and what might be natural to one English speaker might not be in actual to another Americans use do far more often than do Brits.

The correct and more natural sentences are: I already did the paperwork. I did the paperwork already. Explanation: "Did the paperwork" is correct because "to do paperwork" is the appropriate expression. "Made the paperwork" is incorrect because "make" is not typically used with "paperwork" in this context. Natural usage: "I already did the paperwork." (slightly more formal) "I did the paperwork already." (more casual and conversational) Both sentences are grammatically correct and natural, but they may be used in slightly different contexts depending on the formality.