No idea I think they're all really good questions.

I like your example that they become an instance. For the sake of argument say you have Holy Grail AGI™ and you copy it and starting from State t where T is the exact moment you copy it, two instances now exist.

I think they are both "them" but the state change through time as a chaotic process and so since they are now separated they will eventually begin to drift?

This is based totally on nothing but "dude trust me I made it up"