If fuel pump is bad then car would always have hard time starting plus no power in higher RPM's. You should check for fuel pressure regulator because it is responsible for maintaining the pressures. Hard starting is caused because it takes time to bring pressure to required level. When you turn off your car the pressure gets released which should not happen. Fuel rail remains under certain pressure all the time.
Do following tests.
1.Before starting car let ignition switch on before start. If car starts well then it's fuel pressure regulator.
2.Remove the pipe from fuel pressure regulator bottom one. Attach it to transparent pipe and put it in bottle. Just switch to ON state do t start car.
2a.If fuel does not flow. Means not necessary pressure. Check fuel pump or fuel pipe line for leaks or blockage.
2b.If fuel flows turn off the switch. Flow should stop if it keeps on coming then it's leaky fuel pressure regulator.
3.Put back everything and put vacumm pipe on fuel pressure regulator with vacuum machine or with care create vacumm. If you smell petrol or vacumm can't be built this leads to leaky diaphragm fuel pressure regulator.
Sent from my HTC One using PW Forums mobile app