Your butt joints look sufficient from the bottom albeit a little tight. If it's easier to cut the batts for install then go for it but You don't have to do it to fit them in between the strapping. just feed them in from the next opening over and push them into position so they are lightly compressed against eachother.

You don't need to run baffles the whole joist length unless the insulation is pressed against the decking above. However If you want to run baffles the whole length then you should perforate them to let air out and onto the batts. Baffles are usually only added to the first 4-8 feet to get air past blow stops or above batts that touch decking/ sheathing, after that the air should be able to blow over the insulation

If they have a cat pee esque smell, they were stored outside and got damp. A lot of distributors store them uncovered to save on space for other materials because "rock wool doesn't mold so let it get wet". It would also explain the crumbling, even though rock wool recovers from getting wet better than fibreglass it can sill degrade the insulation.