Can low fuel pressure cause stalling?

Yes, low fuel pressure can cause stalling. You can go to Advance Auto ro Auto Zone and they will loan you a testing tool. The test port is on the fuel rail and it is not hard to check. If you are geting any fuel pressure, the relay is okay. The suspect parts or issues are;
clogged fuel filter if applicable
fuel pump is failing
fuel pressure regulator is failing
other contaminants have blocked the line in some way.
The most probable, especially if your vehicle does not have an external fuel filter, is the fuel pump and sometimes the regulator will go bad. Fuel pumps are not hard to change and if you search the site you may be able to find an article on doing so. However, we are happy to walk you through it if it needs replacement.
Any Haynes manual will be more helpful though as it will have pictures that I cannot provide to you. I can only give you wiring diagrams.

The most probable is that the fuel pump

That seems to be low by the specifications chart. But you have to test it at certain RPMs with the vacuum connected and sometimes dis-connected to the fuel pressure regulator.
So, I am attaching a chart to give you the parameters and specifications. I am giving you two charts to cover al engines.

On any car if you find the fuel rail and figure out which side is the incoming gas, follow the rail around until you come to a pot shaped part with a vacuum tube attached. That is the pressure regulator. It controls pressure by holding back fuel which is heading back to go back into the gas tank or what is known as the "return line". Usually on the drivers side but the only true rule of thumb is the first thing I said about folllowing the fuel rail. At one end is incoming gas and the other is returning gas and that is where the regulator is.