Is "Classic BMW" an actual BMW Dealership? I would have taken it somewhere else. Is their any visible coolant? How much are you having to ad and how often?
Im quite surprised the transmission pan would be plastic. Mine is metal. The transmission, if automatic, is actually made by GM in France. The transmission will also have a GM ID number. My E36 transmission is a GM 4L30E transmission also found in the Isuzu Rodeo.