2002 Focus starting problems

My girlfriend has a 2002 Focus ZX3 hatchback, and for quite some time she has had some problems with the car starting, particularly after it has sat overnight. Often, when she first starts it up in the morning, it starts up really rough and the RPMS fluctuate up and down very significantly. Its only after she floors the gas for a little bit does it even out and begin to run normally. It has more of a tendency to do this when the fuel level is below a half a tank, but it does occur when it is above a half as well. It doesn't do this every time, but it does it a lot. Also, the other day, her car died on the away. When she tried to start it up right after it died, a similar thing happened where the RPMs fluctuated significantly but when she gave it gas, it didn't seem to respond. The car was low on fuel (but the needle was still above the Empty). I put 5 gallons of gas in it and it started up ok.

What are your guys' ideas?

Thanks so much

ı think this is a fuel-pomp problem
or your fuel filter may be damaged