I can't really figure out what exactly the facebook API and its services are capable of in terms of user management. Given that I would completely rely on facebook for registration and login, does facebook only provide the authentication and registration process and return me data to store in my own database or does it also itself store a list of already registered user accounts which I can query later on so that I could completely outsource user management from my servers?
If you only need to authorize a User, you don´t need to store anything. You only need to store them in a database if you need to identify returning Users, or if you need to use his data while he is not online.
There is no user management though, you can´t just get a list of all users who authorized your App from Facebook. That´s what you have to store on your own. Make sure to implement the possibility to remove a User from your database, Facebook offers a deauthorization-callback in the App settings for that.