One Small step, a giant leap for Fediverse but...
Day 2 here, and I can see the growth already. Personally I really like the notion of how its gonna shape up in the future but at the same time I really feel for the average user as of now its too complex to understand the working and how the cross servers thing is working. I mean yes still early days, UI will improve further leading to a better UX but the core mechanism yet is little tough to get along. For instance, still unclear if I made the right choice by signing up on lemmydotworld why not lemmydotml , beehaw etc.... and where does this stop? like in the coming times i it would be like a thousands of servers lemmy.this lemmy.that lemmy.etc or anything.anything. That's soo confusing for someone who just wanna join a server. Would be interesting to see how "signup anywhere, its the same thing" evolves.
Unless your instance blocks or is blocked by that other instance, which is exactly what beehaw did to lemmy.world and sh.ithust.works, and exactly what I saw happen a lot on Mastodon.
Ultimately, yes, the server admins have final on what content their users see. Not too different than mods within a community. A user, should they want to, can just make an account on a different server though. Should the user not agree with the content moderation of their original server, and can even migrate all their user data with them most of the time.
AFAIK in ActivityPub everything has an ID (which is actually a URL) that ties an Object/Link to the server it was created on, old things will always live on your old server.