Can authenticaded users publish own content and see only own content? Besides the  module which has many interesting features, what's the best way to allow authenticated users publish content (based on a custom node type), but only allow such content to be seen only by an administrator (an specific role), or that same user only? Such content when published, will only be visible to a role type (administrator) and the user who published it.
For node access, you should set permissions based on role. 

It is /admin/people/permissions on Drupal 7.

Yo can set who can view, edit , create any of your content type based on role.

For more grained field permission based on role, use Field Permission module