The fuel pump fuse is actually a feed to the relay in this system, so it will be hot all the time (it's direct battery power). Once switched by the relay, it travels the rest of the way direct-wired.
Just so we're on the same page, your fuse number is #6 (20 amp) in that in-trunk fuse block, called the PDC. The pump relay is on the opposite side and is the middle of three rectangular (IsO-20) type relays. Terminals are identified from the underside of the actual relay, with terminal 30 being your fuse feed into the relay and 87 being the output circuit. If you were to jumper 30 to 87 it should spin the pump. Checked with a test light or voltmeter with the relay removed, terminal 30 will have battery voltage and 87 will be a ground, since you're reading ground through the pump motor if the circuit is good.
The dark blue/ orange wire at the pump unit (left side pump unit... there are two fuel modules on your Charger) is your pump output. If you find no grounding through terminal 87 at the relay base (in PDC), check continuity to the blue/ orange wire from terminal 87. Should be less than 5 ohms.
I see a fair amount of trouble with the pump units on these cars, where terminals inside the pump module body get hot and lose continuity. I can't imagine why yours would suddenly decide to take that route, but if you find you have continuity to the pump connector but nothing through the pump unit itself, you do have a problem inside the tank.