I've been tinkering with the facebook API. So far, I have working versions of:
Users can login and logout through my page.
Send requests from my app to registered users. Once issued they can be:
updated with new info ("DUE IN 2 HOURS!" or "3 out of 5 questions completed")
read ("A good common practice for Apps on Facebook.com is to detect if a user has any requests pending when your application loads and then prompt the user to complete the actions associated with the requests before continuing.")
deleted (clear request when associated problem set is completed)
Register achievements that can then be awarded to users. They can then be: