Including facebooks plugin causes them to track a whole slew of data about your site, additionally you'll need an SSL cert if you don't already have one, and any information you want to gather from their profiles they have to manually authorize usually in the form of a 'x wants to access your foo and bar data, do you accept?' while logging in, as such it's generally a bad idea to take anything more than you actually need to authentication purposes. You can't not ask for permissions when logging in with facebook as the user has to individually authorize access, usually through a redirection process or a popup if it's a full on app asking for the permissions.
And yes, facebook tracks usage of apps/oauth connections to facebook's information though why this would matter particularly much I can't imagine. As far as I'm aware only facebook and the developer signed up on facebook can access usage statistics, you can likely find more information on this in their ToS.