I just went through the same processes last week, with my new (to me) 318is. I jacked up the rear and spun a tire/wheel to determine if the car has a limited slip. I read on this forum that if both rear wheels spin in the same direction, it is an LSD. I was delighted to discover that my car had one.
I read a post on this forum from a very knowledgeable petro-chemist sort of guy, that he picked Shell Rotella T 5W-40 as the best motor oil for his 318is. It's not easy to find, but from what I have heard, it's worth the pursuit. I just located it tonight at AutoZone.
Redline ATF D4 in the transmission (1.1 quarts) and Redline 75W-90 in the differential (1.2 quarts.) There are 2 types of 75W-90 gear oil, one for LSD and one for non LSD that has an "NS" on the bottle.
17mm bolts are on the transmission for draining and filling, but the differential has 2 14mm allen-cap plugs. I've got a pretty good selection of tools, but I had to go out and buy this one. It also may be worthwhile to buy a suction gun to inject the new fluids.
Tightening torque for the transmission bolts is 37 ft-lb and for the differential plugs, 52 ft-lb.