Being dry won't affect the pump at all, unless you try to run it dry.
The wire trying to "weld itself" suggest a dead pump as well, it doesn't matter which way you put wires on to try to see if it works, as it will spin either way being a dc motor, indeed spinning it the wrong way often works to dislodge dirt/crap/shit in the pump back to the tank but it of course finds it's way back again.
Of course when trying to use it as a pump, needs to be the right way, there is a minute + and - marked either side of the fuel outlet about 3mm in size!!
Whilst the cps signals the cu, it only primes under certain conditions, it's mainly but not just first thing/start in the day, seeems a bit hit and miss when they do though.
I think he is also referring to the brake/abs pump pressuring up when he says about buzzing.
Don't need to be careful or gentle with the relays, you can safely beat the shit out of them, but if they work when doing this it most likely is a relay prob, but might also be a loose connection point in the relay holder, if at suspect just replace with known good ones, they are std type a or type b ones(different pin layout).
There is nothing wonderful about the pumps, have cut these open before, just a regular DC pump, certainly nothing to justify buying bosch over a decent pattern one of another make that's for sure.
tabetha