So, in my headcanon (this might not be accurate to yours) recovery centers work by making a clone of your dead corpse, then reversing it's age until it no longer has damages from whatever killed them. The body then automatically gets possesed by the soul of whoever died. When the soul has a vessel it can't get a new one.
(For example how Tree was able to recover the fish and undo Marker's burns with a time reversal ray)
This is also why loss of limbs is not reversed after death and why Woody still has the peice missing from his head, their bodies were not reversed to a point in time where they still had their limbs/his peice. (The wheel in BFDIA 14 made Pin's body revert to the state it was in from BFDIA 5a to BFDIA 11) (also Lollipop's color wasn't REALLY a part of Gelatin's body, hence why it went away upon death)
If two vessels of the same individual were to be created at the exact universe I think one of two options would happen, either:
The soul goes into a superposition of being in either body until it collapses into being in only one of them (my preffered option)
or the soul now controls two bodies at once somehow.
I've already answered how they reach their alive state but a defective recovery would either be (in my headcanon):
How Purple Face was when X had issues recovering him and/or a severly damaged but not dead contestant (for example a half melted ice cube)
In BFDI the soul appears to be seperate from the character's body, and probably is where the memories are held (the soul probably unconsious in some void while they're dead, since the underworld is the exception and not the norm), recovering refers to retrieving their soul from this hypothetical void, the Yoyelite alloweed Ruby to have a connection with the alive world and recover herself)
as for the final question I think it's a first come firstvserve type of deal? Like if you brought tree back alive his soul would have two viable vessels, his soul would remain in the one he was in first, but would instantly be transported to the other one upon the first one becoming unviable to exist in.
Anyways I don't even know if any of that even makes sense to you but whatever. It's mostly just speculation. (Also recovery in II probably works a little different from BFDI idk)
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