I know a few of these and can speculate a bit on the others to try to give an answer before someone else replies.
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I believe that they just disappear so you want to be sure to choose a home instance you expect to stick around. In the long term if Lemmy develops a way to "link" communities between instances then it would be a way to prevent communities from disappearing in those cases.
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Yes they can have the same username but for your home instance you see the name like "gamer_guy123" without the @lemmy.world but on another instance they would be "gamer_[email protected]". Just like how email works they can have the same username but the domain is different.
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An instance will limit the number of registrations to keep the bandwidth costs down. A lot of these people hosting are hobbyists but believe strongly that Lemmy is the future and are covering the costs which with limited registrations would not be massively expensive. I do wonder how much storage is required though.
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A corporate could spin up a Lemmy instance which would likely be a more stable home instance. Since Lemmy is federated though all the activity can be synced between instances and each instance would be able to control their API so the corporate could lock down the API potentially but other instances would still be able to use their APIs. The concern I would have here is that a single Lemmy instance becomes a walled garden and doesn't federate. That would give them the same control as Reddit. It's up to users to make sure not to centralize under one instance.
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Your home server can block instances if desired. It's important to have a home instance with a policy you agree with. For lemmy.world you can see the list here: https://lemmy.world/instances right now there is only 1 blocked instance.
Hope this helps!