What's the difference between group roles and login roles?
All these questions are basically answered in the documentation.  To be specific:


  A role is an entity that can own database objects and have database privileges; a role can be considered a "user", a "group", or both depending on how it is used.


That implies that internally there is no difference between these, except the LOGIN option.  If you specify LOGIN (or use CREATE USER):

CREATE ROLE dezso WITH LOGIN PASSWORD 'bla';


dezso will become a login role, otherwise not.  You can specify passwords for non-login roles, too - if you later decide to make it a login role, use

CREATE ROLE non_login_role PASSWORD 'bla';

--later
ALTER ROLE non_login_role WITH LOGIN;


You are right when saying 'it's only possible to authenticate with login role'.  Note, however, that a password is not always necessary - if you use anything else than the password or md5 authentication methods.  On the other hand this means that a role without the LOGIN option set cannot log in in any way.

Finally, you may set rules in pg_hba.conf for non-login roles, but as it's used only for authentication, those roles will have no effect (unless you enable login later, as above).