if the fuel pump is shot,how can you start the car, i mean doesnt the pump push the gas to the engine?
if the pump is making a high whiiiiiiiiine noise it is near its end life, i doubt cleaning will fix it, but you can try, that is one reason not to leave the tank to reach empty level, it heats up the pump thus shortening its life span and all the crap from the bottom gets sucked into it.
dont put gas from "unknown" gas stations, well gas in the usa is crap in general but a top tier station will have a better quality...i assume.
have you replaced your fuel filter also, general tune up, that might fix the idle issue, check for vacuum leaks, especially the boot going to the throttle and air box (MAF).