1993 Pontiac Grand Am Short in Wiring?

Electrical problem
1993 Pontiac Grand Am 6 cyl Automatic 171000 miles

I have a '93 Pontiac Grand Am SE 3.3L with 171,000 miles. I noticed when I turn the steering wheel right the left side of my car speakers and the bass in my car would go out, but when I turn the wheel left it would come back on. My heater core went out about the beginning of summer and I had it replaced. Since it is getting colder at nights I decided to turn it on. When I did this, my ABS light and fasten seat-belt light comes on. Also, the headlights flicker off and on and my speedometer starts jumping up and down. Then eventually it dies. When I re-start the car, everything has reset, radio stations, the clock. As if my battery cable came undone. I checked it and all seems normal. I also notice that when I turn the key backwards and open the driver-side door the radio works fine. But I can hear the short in the speaker when I close it again. I also need new brakes desperately, and now I am starting to notice when I am coming to a stop my lights flicker and my car wants to die. (And sometimes does.) I am desperately wanting to fix this problem. Can anyone help! ASAP! Thanks.