BuddyPress.org

1.) yes, the group admin can add other admin/moderator and ban users

2.) they need to join your group, then under group memebrs you can add them as an admin/moderator

3.) this is possible yes, I accomplished this by adding <?PHP if is admin ?> into the bp-core to hide the create group button from non-admins (your community will want the ability to add groups though)

4.) you can create “private groups” that are visible to everyone, but you can only join if you’re accepted…

why don’t you create a couple different types of groups, then you’ll see all the features/abilities they have