Idk about your specific case but I do know being logged in to another user can happen on buggy servers and has happened to others.

Servers have to keep track of which clients are logged into which users, usually via a session token. Memory corruption or a race condition can cause one token to be associated with another user.

Definitely possible. Steam had something similar a while back caused by caching issues [1]. I have no idea about Facebook specifically though.

[1] https://www.forbes.com/sites/insertcoin/2015/12/25/steam-is-...