Who has their message moderated
You can choose who has their messages moderated in two different ways.
You can specify that everyone has their messages moderated, apart from a specified list. Or, you can specify that only certain people have their messages moderated. This is set from within the Moderation page of your group Dashboard.
You can choose who gets moderated or not on the Moderation page but you can also do it from within the Members page. With moderation enabled if you select a member for the Members list then on the right-hand panel there's a "Moderate this member" checkbox to toggle whether they get moderated.