"wear" only refers to clothes or accessories and the like. Anything else taken from one place to another is "carried". German "tragen" means both.
If I want to say that the man wears the girlfriend (don't ask how) which word should I use?
Well, that is "tragen" or "anhaben". "I am wearing a dress." - "Ich trage ein Kleid. / Ich habe ein Kleid an."
the man carries? i would read that as the man wears his girlfriend. am i mistaken?
Stupid question but why isn't it "den" instead of "die"?
Because the girlfriend is a feminine noun (die Freundin) and it is the thing that he is carrying (akkusativ, therefore die and not der).