I rebuilt my bottom rear door hinge a few years ago. The cover is separate, but is tack-welded to the hinge leaf, so they both "slide" in and out together.
Trying to remember how I got the hinge leaf out of the door slot . . . big fun hammer? (Is that what BFH stands for?) It came out hard the first time. I got the hinge together wrong, but the leaf came out easier the next time.
I have some pictures, but I haven't mastered posting them. You can e-mail me and I'll send them, and try to anwer your questions. That will give me time to look up my records.