The E46 is not quite a Morris Minor. The vehicle is very intricate, especially by contemporary standards. Uncertain.
The peculiar occurrences are attributable to the car's radio, which is not a conventional model but rather a module linked to the i-bus, one of many internal data networks included in the e46. Additional modules linked to the i-bus include the instrument cluster, light control module, among others. Many components in the vehicle are interrelated, serving numerous functions; for instance, the radio antenna also functions as the key fob antenna and the rear window defroster. The antenna is linked to the radio by the k-bus and the i-bus.
If the new radio is interfering with the i-bus, it might lead to apparently unrelated malfunctions in the key fob and instrument cluster.