All sites or applications connect and work normally without any problem.
Except Facebook, Facebook not only connects nor by the application and not by Safari or Google Chrome.
So I think it has something bloquendo either DNS or anything else. Because when you use a proxy site, he enters, however, can not do anything.
Using FaceTime http://support.apple.com/kb/ht4319
Troubleshooting FaceTime http://support.apple.com/kb/TS3367
The Complete Guide to FaceTime + iMessage: Setup, Use, and Troubleshooting
Troubleshooting FaceTime and iMessage activation
iOS: About Messages
Set up iMessage
Setting Up Multiple iOS Devices for iMessage and Facetime