Yes you can access those values using several methods. In order to get the provider, i suggert you using this code:
FirebaseUser firebaseUser = firebaseAuth.getCurrentUser();
if (firebaseUser != null) {
for (UserInfo userInfo : firebaseUser.getProviderData()) {
if (userInfo.getProviderId().equals("facebook.com")) {
Log.d("TAG", "User is signed in with Facebook");
}
if (userInfo.getProviderId().equals("google.com")) {
Log.d("TAG", "User is signed in with Google");
}
}
}
There also other methods which are very useful: getUid(), getDisplayName(), getEmail(), getPhoneNumber() and so on. please take a look at official documentation.
As a conclusion for this question, there's no way in which you can call another method to get the email address of an user. What can you do in stead, you can create a users section in your Firebase database, store all data you need and than just query it.
Hope it helps.