You are not speaking to Apple here, just other users.
Reboot device by pressing both the home button and sleep/wake (power) buttons at the same time for 10-15 seconds until the apple logo appears on the screen, then let go.
If that doesn't work then reset the device by going to settings/general/reset/reset all settings (or for network connection issues 'reset network settings').
(no media or data will be deleted from the device, this will only take a minute).
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
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Using FaceTime and iMessage behind a firewall
iOS: About Messages
Set up iMessage
iOS 6 and OS X Mountain Lion: Link your phone number and Apple ID for use with FaceTime and iMessage
How to Set Up & Use iMessage on iPhone, iPad, & iPod touch with iOS
Troubleshooting iMessage Issues: Some Useful Tips You Should Try
Setting Up Multiple iOS Devices for iMessage and Facetime
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Unable to use FaceTime and iMessage with my apple ID
FaceTime, Game Center, Messages: Troubleshooting sign in issues
How to Block Someone on FaceTime
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To send messages to non-Apple devices, check out the TextFree app https://itunes.apple.com/us/app/text-free-textfree-sms-real/id399355755?mt=8
How to Send SMS from iPad
You can check the status of the FaceTime/iMessage servers at this link.