We have our instance configured such that the account registration permissions are " Visitors, but administrator approval is required". Do administrators get a notification when a new account is created, so that they can approve it? If not, is there a way to set that up?
You have to configure it.
This is pretty easy, you can for example have a look here: https://drupal.stackexchange.com/questions/21359/administrator-notification-on-user-registration