BuddyPress.org

Buddypress has no privacy/security controls whatsoever. There is also no built-in way to consistently use real names and let people register with first and last name on sign-up, which will probably become a problem for a school application.

Buddypress is basically an evolving hobby project by PHP programmers. You may have more luck with a more user-focused semi-commercial script like Social Engine: http://www.socialengine.net/