Can I run the fuel pump 24/7 continuously why the key switch is on and the car is running

The fuel pump is only supposed to run for a couple of seconds once the key is first turned to run, to prime the fuel system, but you should still have fuel pressure at the rail.
How much fuel pressure do you have at the rail or are you just pressing in the shrader pin checking for some fuel pressure and there is none at all, or are you just perhaps assuming that and actually there is no fuel injector action?
Why would you want to run the fuel pump 24/7?
It will run 24/7 once the engine is running.

PATENTED_REPAIR_PRO is correct, the pump will cycle and build fuel pressure with the key on then switch off, once the engine I running, the fuel pump receives voltage while the ignition is on and alternator is charging, pump will drop out with key turned to off or engine stops with key on (safety precaution so fuel will not spill in the case of an accident and the fuel system is damaged). You need to test fuel pressure static and running to determine if there are any faults in the system with pressure regulator, pump or filter restriction.