Are you looking in the correct place?. Drain plug should be lower at bottom and fill plug is on the side slightly higher always loosen fill plug first for obvious reasons
No gearbox or diff has lifetime oil theres no such thing what bmw should put on their lable is once your component blows up that's its life over due to you not maintaining it correctly ie.change oil every 70k miles
On mine (2006 3.0si) there are two plugs on the box. Fill plug half way up the side (off side of the car) and the drain plug underneath on the bottom. Diff only had a fill plug. Again half way up on the back of the diff.
Deffos change the oil. Mine came out of the box on 84K and was black. Box is now a lot smoother.