If a registered classmate clicks on one of the Missing names and then sends them an e-mail invitation, does the Administrator get any type of notification of the e-mail that it went to and for which name?

No. It's a privacy issue. Somebody goes in and invites somebody else, but they're not intending to send the Site Administrator somebody's private email address. If we released those email addresses there's a 100% probability that some Administrators will start sending emails to those addresses. Although I realize this wouldn't be an issue with most Admins and Classmates, it is for some. We can only give out somebody's private email address with consent and there is no consent here.