Yes, all of those social graph relationships are hinged off a permanent identifier (DID) and everything comes along when accounts migrate PDS instances. Folks can use zeppelin.social from any PDS instance. The DID PLC directory is currently hosted by Bluesky, but the directory can be forked, and did:web identifiers can be used as an alternative (and several independence-minded folks in the network do so).

Migration between servers is so seamless that is causes confusion and doubt that the protocol even supports migration, because there is basically zero in-app visibility of which users are on which server.

Yes, the network continues to work on zeppelin.social if Bluesky servers are down.