Looks like there is a timer or something that separates infections, that means you can't get infected right after you got "Des-infected" by the death of the gravelord. I say this because after killing the gravelord and stopping the curse, when I was back in my world I used the Dried Finger, and the INSTANT I used it, 2 BPs hollow soldiers appeared and a sign next to them. It was the same gravelord I killed before but he started channeling the curse again. I killed him again ( ) and then the curse stopped again. Back in my world I used the dried finger once more, I didn't get infected immeadiatly but after a while the BP hollows appeared. This time I took them some photos, after a while, a message appeared saying that the "Disasters" are gone and all that and in the same instant the BPs died (not disappeared, they awarded souls).
BPs have the same drops their standard versions have (the bps hollows dropped their broken shields, it's not a 100% drop anyway).
This something almost everyone knows but just to state it, BPs respawn when resting at a bonfire.
When killing a gravelord in their world as a spirit of vengeance you get a Eye of death.
Nothing else. Thanks for reading!
P.S: I'm going to upload some photos of the black phantom to the gravelord covenant page in the wiki.