Yes

The 3e- of each Li are indistinguible and all contribute to the observed local 0.5 (spin up + spin down) probablity. They are entangled but not just n electrons.. all are if you treat the system like a FCI wavefunction. So yes, fragments should be entangled that is my guess

For H2 I think they should but for any other system you cannot really say what pair of electrons forms the bond. All participate in the bond when you think about the FCI wavefunction. Same for the cleavage, if you break H_n you get n electrons entagled, but if you break Li_n

Looking forward to meeting!

Enhorabuena 👏👏