The fuel pump relay is where I would start looking if the pump does not run when the key is on.

As said by a previous poster, the pump runs for a couple of seconds to pressurize the system before starting. You should hear it every time trhe key is turned to the "ON" position, not the "START" position. If you do not hear it, you have a blown fuse or more likely a bad relay since it starts sometimes.

IRT your other question, the filter is in the same fuel cluster as the pump.