I would take it to an Apple Store for a thorough diagnosis. If that’s not possible then call Apple support and there’s stuff they can do remotely to see what’s going on.

Unlikely. Have you changed your passwords? If not then do so immediately.

I don’t know your age so this might not apply to you but per a parent is monitoring it?

I always go with an unlocked one because it’s easier to sell it when you get your next one.