Re: Why is it inheriting from Registered?
My first reaction was that it is a bug. But then I thought maybe it's a design decision. After all, why would a new group be able to do less than an anonymous user or a basic registered user? The person could just log out and have the permission he/she didn't have when logged in. Also is there a conceptual problem with a subset of registered users being denied permissions that normal registered users have? This may be the reason why all new groups inherit from anonymous and registered by default (and no way to change).
If you really need such a configuration, I suppose you can edit the database table (don't know the name offhand but can check if necessary). If there is a compelling reason for admins to have the option, maybe you could describe what your configuration needs are (to show what the design decision fails to consider) and submit a feature request at dev.tikiwiki.org.
-- Gary