1994 Toyota Tercel Suspected Electrical?

Hello. Been having a slew of interesting problems over the past month. In the beginning, every time I would turn on my turn signal my CD player would short out. When I turned on my headlights, the whole engine seemed to "shake" once. This eventually subsided and I didn't have this problem again.

Then my dash stopped lighting up. But when I hit the hazard lights. It suddenly turned back on. Driving on the turnpike for about 300 miles I didn't notice any problems. Then I got to my destination. And the radio started to turn on and off and on and off and my headlights got weird and the car started to sputter and it turned off (but not like I let the cluch out or anything, completely different from stalling out) I was able to restart the car and drive to pep boys. Tested the battery and alternator (both are fine).

I'm worried about driving back home (about 150 miles) before getting this checked out, but I'm not really familiar with the area here. Concerned about the car turning off again on the turnpike. Any ideas?

Thanks!