Oil wouldn't burn off the friction plate - it would tend to aborb into the material, and make it become somewhat friction-less. The material is fairly dark in color, though my write-upr in the wiki is with a 1982 that uses the newer style clutch assembly, so it looks a bit different. Someone will likely chime in soon with some pics of a 79 clutch.
The bell housing does tend to end up with alot of crud in it, but if there is an oily mess on the bottom then there is definitely either a rear main seal leak or an oil pump cover gasket leak - if you do decide to take the flywheel off BE SURE TO BLOCK THE CRANK FROM MOVING FORWARD FIRST by sticking an extender bolt into the front of the rotor, or block the rotor end from moving forward with some other means and putting the front cover back on and tightening the bolts up just enough to keep it all in place - you don't want the crank moving forward at all when you are pushing on the flywheel/bolts in the back.
I would only use BMW parts in the clutch. You should measure the pressure plate for runout, as well as the friction plate thickness as you may need to replace more than just the friction disk, especially if high mileage engine.