Are These Problems Related?

[bob v]

Okay, I get this great deal on a '95 Impreza (2.2 liter, auto trans) for my daughter. New plugs and wires banished the check engine light. But, I have a problem with the radio and the fuel gauge. I didn't think they were related until the radio really started acting wacky. The fuel gauge runs down to empty when I have a half of tank left. I assume it's a bad sensor in the tank. The radio didn't play unless the car was hot. It didn't play at all when I first picked up the car, but the first day I come out of work to a hot car, the radio is working. I stop on the way home, get back in the car, and the radio doesn't work. This scenario plays out for a few times, so I figure there is something bad in the stereo itself. However, today brings a new wrinkle. Just like always, the radio works when the car is hot, but now when I'm at a stop light, the radio dies until I pull away from the light. After a couple of time of this, I put the car in neutral, rev the engine slightly, and the radio plays. Let the revs die, and the radio stops. Normally, a radio plays, or it doesn't. It shouldn't be dependent on engine speed. By the way, there is no alternator light lit on the dash. Could the problem with the radio and the fuel gauge be related? Maybe a bad ground? Could the radio issue be caused by a bad belt, or alternator problem?

Any comments on how I should approach this would be appreciated.

Thanks