What is wrong with my 2000 chevy impala?

I have a 2000 Chevy Impala. I had to replace the fuel pump at the end of April this year. The car ran great for a little over a week, but shortly after it started acting up on me. After about 15 minutes of driving or if I make frequent stops, the car will kind of stall or act like its overheating, but the heat gauge is only about halfway. I will just be driving along and suddenly it is difficult to get the accelerator to cooperate. I will floor it, but it will sputter. Once this starts to happen the car also starts to buck along a bit. It suddenly makes a high squealing noise, as if a belt has slipped, and I suddenly lose everything. My power steering goes and the accelerator wont do anything. I do however have full battery power. My lights work and the radio works too, but on the dashboard a big red battery light pops up. I typically have to pull the car over and turn off the engine for about 15 to 20 minutes. After letting the car “rest” for 15 to 20 minutes, it will start back up and run for about another 15 minutes before having the same problem all over again. Lately, I have noticed that the car does not seem to have this issue as frequently when it is a cooler temperature outside. Also If I do not make any stops, and the stop lights all stay green, I can usually make it all the way to my destination without incident.