As far as I know, anyone can install the open source packages and run a server (don't quote me on this, I'm very new to the platform). I assume your info would be lost, but idk. Maybe it's decentralised across mirrors like a torrent? Idk if it is, but it should be if it isn't...
Yes, anyone can run an instance.
If your accounts home server/instance shuts down, the account is lost. But your posts and comments should still be on other server. If I understand federation correctly, each instance keeps copies of the posts and comments from instances it federates with.