The engine oil can be checked either through the settings menu on the iDrive (if you have a nav screen) or through the turn signal stalk (if you don't have nav). Not entirely sure how to check it through the turn signal stalk since I have iDrive, but a quick search of the forum should produce an answer. As for the transmission, the oil level can not be checked through a dip stick either and can only be checked at the transmission itself and would require a lift or a jack and jack stands.
'07 335xi, Alpine White
| Cold, "Sport", and Luxury packages | Tinted | OEM Black Lines | JB4 | DCI | ER FMIC | Forge DV's | Custom exhaust with secondary cat delete, Magnaflow mufflers, black Dimisa Tips | Staggered 18" V718's, Matte Black | Flappy Paddles | Titanium CF Trim Wrap | BMW Performance Shifter and E-Brake Handle |