The warm-up pressure is good but the other pressure is not of much use other to say that the pump was running. It does sort of show the injector opening pressure and it tells me that the fuel pump was running at the time as residual pressure (that to which the systems goes instantly when the pump stops) is 3 bar.
The car will run without power to lambda control module, frequency valve, and warm-up regulator. it will not run more than an instant without the fuel pump as the main pressure regulator has a dump valve to instantly drop pressure to the residual value to prevent dieseling. (this pressure is below injector opening pressure - so no injection).
If your car is running with the fuel pump relay removed I would find out where the power is coming from. I suspect you are on the wrong relay or the wrong relay is being used. The fuel pump relay on that model is similarly shaped (to all others) but has 6 pins instead of five if I recall.
Bosch Master, ASE Master, L1
33 years MB technician