I want to make a Xamarin.Forms project, targeting iOS, Android and Windows Phone.
My app needs to authenticate users using Facebook.
Should I implement login
You could consume either Xamarin.Social or Xamarin.Auth for that. It allows using the same api whatever the platform is.
As of now, those libs aren't PCL yet, but you still can consume them from a Shared Assets Project, or abstract the API you need in an interface and inject in with DependencyService
or any other DI container.