Hi,
To log in to Facebook, we do not need his email or password we just need to call a Facebook API from unity which we can easily do.
After the user is login to facebook we can get his or her email id and can save to out an application.
Freind list of the user can easily obtain once he or she allow us required permission which we have to ask them.
Please ping me if you have any question looking forward to work with you.