If you click on Communities
and select All
, it allows you to search for Communities across all of Lemmy-Land, not just the instance that you've signed up on. I think that every instance can have its own separate community with the same name, but in a lot of cases that may even be desirable.
As far as moving users/communities between servers, that's Nomadic Identity. As far as I know, the only Fediverse project that implements it is the Zot protocol that Streams and Hubzilla are built on. ActivityPub does not support and it's not on the roadmap as far as I know.
You should post this in the calculator community!