Help needed !!!! (mini cooper 2002)

[Szouein]

Hey guys i recently bought a Mini cooper 2002 with 85000Km on the clock .
1st everything seemed to be normal until i noticed that the car cutts power while driving it randomly at any speed .
I asked my mechanic and he told me that it might be happening because of dirt passing through my fuel system so he asked me to do the folowing :
1st step : add fuel cleaner solution in my fuel tank and drive on high rev for a while if it dosnt work then proced to step 2 .

2nd step : Replace Fuel filter , and when i came to this part i discovered that my mini didn't have the old filter system converted so i replaced the old system with the new one , and when i did nothing happened the car still have the same problem but this time more often and sends the car sometimes into a sudden stop.

I tested the fuel pump pressure and it indicated a 4 Psi .

Mechanics are now confused if they should replace the fuel pump or check if there is a problem with the fuel pump relay !

what do you think guys ?? :S
I am really confused and i don't know what to do + were i live there are no Mini cooper experienced mechanics
I need guidance !!!

HELLLP! !!!

P.S: The car comes into a sudden stop even if its on a high rev and at any gear , the rpm would just die with a small "chocke" feel , and sometimes the event dsnt last long and the car relaunches quickly and gain quickly a high Rpm reading .