He wasn't losing limbs as far as we know but I guess they decided overtime that he was deteriorating physically. Freeze being just a head did indeed prove to me that he was immortal (how did he go on without organs?). You o have to admit that his "redemption" in Batman Beyond was a GREAT ending for his character.
As much as the TNBA Joker design gets hate, they blended the best traits of both designs together to make pure gold. I just watched Mask of the Phantasm and I just remembered how good it was. Joker was incredible in the movie and they were really able to let his 90's censorship leash loose in the movie. They also let him kill more people in TNBA but they never say that the people are dead but it is kinda obvious when we don't see the people again.