you can use a mozilla.com user id to talk to someone with a matrix.org user id, or a kde.org user id
all servers are equal participants in rooms, so a room doesn't live on a specific server aside from servers being able to create friendly names pointing to them, but nothing stops #foo:kde.org from pointing to the exact same room as #bar:mozilla.org -- both servers are participating equally and have their own shortcut name to the room
Being able to leave one server and join another while maintaining an identity (say, a public key for instance) is on Matrix's to do list, they haven't decided how to do it yet afaik.
edit: Okay, not actually webfinger. But [0] has instructions for the `/well-known/matrix/server` way. It only talks about subdomains, but it should work across domains. Possibly also with the SRV header.
[0]: https://github.com/spantaleev/matrix-docker-ansible-deploy/b...
No.
Matrix is like chatting via GIT (distributed databases) and tends to be a great team messenger like Mattermost or Zulip - XMPP is structurally like email ...
And I'd say that Matrix is closer to e-mail and XMPP than you seem to assume. Once the database is synchronized, it works pretty much the same way. Only if a missing message is detected in the graph, then a server makes another request for the messages it missed (backfill).
Moreover, Matrix and Git are quite different, since you want to be pedantic. Both the synchronization protocol, and conflict resolution are handled differently (Git does very little, Matrix is more like a CRDT in that respect).