1999 Mercury Tracer Improper grounding?

After buying a '99 Tracer wagon with a salvage title, I expected some problems (like the bent rotor on the front driver's side, which is where the damage was, and the improperly aimed headlights, which I can fix myself). I didn't expect that my radio would be almost unusable when I'm driving; with the engine running, a constant level of interference can be heard on the radio, a static hiss that seems to coincide with the engine timing. It has a rather loud exhaust leak under it, somewhere between the manifold and the catalytic converter, but I've driven cars with worse leaks than this and never had static result from it. The gas gauge also drops very fast; after filling up just a few days ago, I find that I've mysteriously lost half a tank of gas, yet haven't driven more than 25 miles, if that. I can't smell a fuel leak anywhere, so my guess is that the gauge is just wrong. On top of all that, the dome light doesn't consistently come on when set to "Door" and the alarm randomly goes off if I arm it (which, thankfully, I don't; not since finding that out). Hopefully, someone can help me diagnose at least some of these problems without spending a day or two at a shop, getting charged by the hour.