I think some realistic diagnostics are in order here. The ECU and other modules in these cars simply do not respond well to filthy or low voltage. I'd be cleaning the battery posts, battery cable clamps, etc.
I'd be considering a new battery. (Any who says, "Have the battery tested" should be ignored).

I'd then measure the fuel rail pressure, in fact, I think I'd do that first - there is no reason to be guessing about the pump or filter when it's as easy to measure fuel pressure as it is tire pressure. The engine has NO SENSOR to tell the ECU what the fuel pressure is, pressure is assumed and if it is too high or too low, the ECU has little to detect that with, other than the O2 sensors.

I'd wonder about the throttle body as well, but fuel pressure is vital and is very easy to measure.