As to the moderator role, please read this articles from our user manual, to get a better understanding how it works
http://docs.oxwall.org/user-manual:privacy:moderatorshttp://docs.oxwall.org/user-manual:privacy:roles
http://docs.oxwall.org/user-manual:users:user-roles
as to the groups can be seen by admin - Do you mean you can't see some groups or can? Because admin sees every group, disregarding whether it is private or public