Fuel/accelerator problems. dies when accelating or at idle. runs when accelerator held in one position for a short while.

Have you ever changed the spark plugs? If not start there if that doesn't take care of it remove and clean the MAF sensor located in the air filter housing. I hope this helps. Take care.

fuel filter

if the coolant level is going down you may have an intake or head gasket leaking coolant into the cylinders pressure test the coolant system

i think this car has a vaccum activated fuel pressure regulator could be your problem also a large vac leak would do this as well

It sounds like there is a problem with the Idle Air Control (IAC) valve. Its job is to open and let air into the manifold when the throttle is closed at idle. If it does not open, the engine dies at idle. The IAC is mounted on the throttle body. Possibly the valve is clogged or stuck, in which case it could be ok again if it is removed and cleaned. Or it is broken, and needs to be replaced. Or, there is a problem with its electrical connection, that needs to be traced. Good luck, let me know if you have any questions.

the problem is a fuel injector one or more is clogged up replace fuel injectors or run a good fuel injection cleaner lucus fuel injector cleaner will be sufficiant

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Research the trouble codes.....my '01 had a similar problem, turned out to be the CPS (Cam Position Sensor).
Easy fix.....10mm nut and unplug/plug in and reset codes and your done.
Dealer item.

idle speed sensor maybe bad. check for codes

First thing I'd check is fuel pressure. 55psi

You may also have issues with your air flow meter.Generaly though this symptom is usualy a fuel pressure problem.This test may or may not work depending on wether the fuel rail is the problem or the pump.Squeeze the fuel return line at the back of the fuel rail and if engine improves the fuel pressure regulator on the fuel rail may be faulty.If no improvement its likely the pump.The best and most accurate test would be to use an inline fuel pressure tester.Can you hear the pump pumping up to pressure when you turn the ignition on?Usualy though the pumps fail but can be heard running but unable to maintain pressure.