How can I check the fuel pump relay to see if it is working

--Try swapping it with a like one or get a multimeter and measure the relay's coil and switch side-coil side should be 40-80 ohms and switch infinite/o ohms-

The pump relay primes the fuel system for about 2 secondsd when the key is in the, "ON" position, before you turn it to, "START".
You might have to have someone else listen near the gas tank and on the drivers side for a whirring noise while putting the key into the, "ON" position. I tmay be heard to hear in your car because Mercedes does such a good job of deadening noises, but they should be able to even though they may have to get essentially under the car or at leaset lie or crouch near the tank. So, get them to listen for the whirring noise when you put it into, "ON" and don, t turn the key to start they car.
If it is whirring or priming the fuel system, the relay is working. You can pull the relay out and put 12 Volts across the resistor side which actives the switch ont the other terminals which you can check with a multi-meter for continuity when the 12 volts is applied. Cointinuity will show that the switch is thrown and the circuit complete.
If you ontinue to have fuel pump issues or are not sure about what is going on, I am not certain of your problem but this is if the car runs, go to Advance Auto or Auto Zone and they will pull trouble codes for free. Then even if nothing comes up and it si performance issues you have, test the fuel pressure. The same 2 parts stores have test gauges on a lonaer basis and there is a test port on the fuel rail. If you need any further help, come back and we are always here.