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.
Can anyone run a server? If our account is pinned to one server and that server shuts down, I assume we lose all our account info/history?
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.