I get that searching can be a bit finicky sometimes but doesn't typing in a full username of a user you want to search for usually do the job?
That part about shutting down is something that https://joinmastodon.org/covenant tries to help with, where advance notice should be given and multiple people should have access to administrative actions. At least if the server has to shut down the users are given enough time to look at another server.
There is Funkwhale that you can use for self-publishing music. You can also upload your music library privately to listen to remotely.