I have a 1991 Chevy Corsica 3

I have a 1991 chevy corsica 3.1L, someone pulled out the fuel pump and injecter fuse. The car was running still and the fuse was on the floor. Is the current suppose to still be flowing? The car was surging and popping I put the fuse where it belonged the problem had stopped. That night the battery light came on and the next morning took it to autozone they did a test the battery was good but the altenater was shot the battery had 50% charge I drove about 42 miles on the battery to get it worked on. Found a good altenator put it on started the car twice it was popping 2 times then battery dropped I took it to autozone they said the battery went bad. The car would crank but wouldnt start. And no sound from the fuel pump. I check the wires to the pump they was melted. I cut the ends off and redid the conector to the pump. Sometimes the car will start and drive fine, other times it will jerk and cant even do past 40mph. What are the chances that the wires from the fuel pump to the injectors, to the computer, to the fuse box got fried? Can this happen? And can this short out the fuel pump and the fuel injectors aswell?