Hi CharlieC
There's no way of telling what a motorhome converter has done, unless you can get hold of a schematic. However, it sounds rather unusual to me to have all those items functioning without the key in the ignition and turned on or to the accessory position.
It's not unusual for the radio power arrangements to be different in a motorhome, because people are more likely to listen for long periods. So you may find the radio is powered from a permanent 12V feed from the vehicle battery, or sometimes from the habitation battery.
One thing you could try is to temporarily disconnect the habitation battery, and see if the circuits you mention are still live. If they go dead, it would point to a wiring error in the motorhome part rather than the vehicle.