I'll try and answer your last question first. Regards the heater it might well be the ballast resistors to the heater motor have gone belly up. These unit consists of different windings and all but one may have failed. If you do a search of the forum for heater resistor or such you should find loads of posts an dremedies on the subject.
As already said it looks like your radio has no permanent voltage supply and therefore can't hold its memory. When fitting the after-market stereo did you use an ISO adapter??