Which are correct:
1-The man writing reports last week is my friend.
2-The man who wrote reports last week is my friend.
3-The man writing reports last week was my friend.
4-The man who wrote reports last week was my friend.
They are all supposed to mean the same thing. I am still friends with that man.
Since it was last week, you should use "wrote." If he's still your friend, use "is."
I suggest the sentence would be improved with something like "those reports" or "the reports we just read" or something other than the grammatical but unnatural "reports" alone.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.