I like to clean rust with oil, or solvent. I have used a green scrubber pad many times, that has some wd-40 or even oil on it The cylinder is removed by unscrewing or poking a metal retainer that is located inside the shackle hole. Some of those retainers need to be depressed while pushing the cylinder out, so it can take that 'third' hand which is all too common in this field
Yeah, I think vinegar will work. I generally disassemble, and brush parts clean. When I do use chemicals though, I use rust remover. For gunked up locks, I alternate between degreaser and penetrating oil.
I use an ice pick in one hand and push out (press down) on the rear of the lock cylinder (brass part next to retainer) with something else, while the lock body is held in a vise. A little cussing seems to help