User registration approval/activation
There is no current way that I know of that does this, but you can probably do it relatively easy with a custom plugin.


If e-mail validation is turned off in the Users settings, the created user is verified by default. You can hook into the users.onBeforeSaveUser event and set the status as UserStatus::Pending. Then redirect them to a screen saving something like "Blah blah you will be notified once we activate you blah blah".
Hook into the users.onSaveUser event, check if this is a new user (isNewUser) and send off an e-mail to a given e-mail.
Admin logins and activate as normal.
(Optional) In the same users.onSaveUser event, if this isn't a new user and the user status is UserStatus::Active, send out an e-mail to the address given by the user.