As Cristian said, fbrocket predates the official SDK and is more or less obsoleted by the official SDK, which is newer, shinier, and mostly based on newer longer-support-lived standards like OpenGraph and OAuth. FBRocket is supposedly being rewritten for these, but there's no release for that yet AFAIK. There's a few things the official SDK is still missing (photo uploading, for instance) but if you just want sign-in-via-facebook, it's definitely the way to go.
I'm not sure I understand your 3rd question though -- you need to include Facebook code, either by a jarfile, android library include, or copy-paste -- in order to actually call the Facebook APIs. The Facebook project is open source; if you're not comfortable including it wholesale, you can freely yank out the bits you need. For example, I've used it in projects that only needed authentication and not publishing, customizing the auth dialog handline and removing all the non-login-related code. You could roll your own implementation based on authenticating via OAuth2 and call all the endpoints yourself, but why bother when Facebook already did the work of giving you the code to do that from Android already?