sword of totsuka probably cannot be absorbed becus its not ninjutsu its a sealing sword that traps a person in genjutsu for eternity that is the probable reason why he could not absorb it, but anyway the bodies can be sealed its not only the soul but the body also when itachi used it, it absorbed nagato's body inside the gourd as well not his soul only. But u are right that mobility is something that they gain as pain and their eyesights are better, but the thing they do lose is speed and the power of the techs.
I guess, but logically it shouldn't be able to seal dead bodies which lack souls. it cannot seal trees, land, or anything without a soul. which is why itachi waited to seal orochimaru directly instead of just stabbing the head of the hydra. stabbing the hydra wouldn't have done anything since it lacks a soul of it's own. orochimaru has a soul, and he was sealed. nagato had a soul, and he was sealed.
Preta path should be able to absorb the sword. if it was truly a spirit blade, then it couldn't actually cut/pierce through physical matter, but it can. the spirit blade is (probably) converted into a physical chakra based form when equipped to susano'o, making it vulnerable to Preta path; that's why it was physically able to pierce through Orochimaru's mid section. The Death God was truly spiritual, as it didn't actually physically do damage to the person's abdomen during the sealing process. Also, the preta Path has shown to absorb even natural energy (when master-locking naruto).