1) Have you followed this solution?
? So far I know moderators are 100% able to activate user's membership from the profile. So the only thing for them needed to know is that new user has been signed up, i.e. moderators should receive email notification about it, the same as admin. I think it would be possible to implement such thing at the add-on level.
Additionally, pre-moderation add-on
would give you some more functions regarding approving the new users and their postings.
2) In admin panel, click "Search Users" and then choose from the dropdown "Member: [No]" - it will mean you're selecting only inactive users straight away.
3) Doesn't seem clear for me what do you mean. If you click on user's "Member" title under his nickname (for example like in my post here - 'Team member') you go to the user's profile straight away. If user has no such profile, it means he's posted as Guest.
4) Users naturally won't be informed about this (and I doubt it would be really necessary). However we could program some kind of custom add-on for this as well.