No worries, happy to answer as much as I can!

I'm not quite sure what you're asking here but I'll try to answer it anyway:

Every time you add or remove a relay, an "event" with your list of relays is created and signed by your private key and then sent to all the relays you have selcted. So let's say you log out of your favorite nostr client and then log in again, your nostr client will fetch your list of relays and connect to all of them (some clients may behave differently). As long as these events reach your relays, your data will be available as long as the relay is up and reachable.

"Logging in" on nostr really just means that you identify yourself by your public key so that the client can fetch your own events/data. And if you give it your private key, you'll be able to sign new events, i.e. write a new "tweet" or encrypt/decrypt a new DM. Logging out is just clearing the public key or private key from the client itself.

If this didn't answer your question, don't hesitate on asking again.