Is the whole iPad frozen or just that app ?
If the whole iPad then try a soft-reset : press and hold both the sleep and home buttons for about 10 to 15 seconds (ignore the red slider if it appear), after which the Apple logo should appear - you won't lose any content, it's the iPad equivalent of a reboot.
If just the Messages app then try closing it via the taskbar and see if it works when you re-open the app : from the home screen (i.e. not with the Messsages app 'open' on-screen) double-click the home button to bring up the taskbar, then press and hold any of the apps on the taskbar for a couple of seconds or so until they start shaking, then press the '-' in the top left of the Messages app to close it, and touch any part of the screen above the taskbar so as to stop the shaking and close the taskbar.
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: FaceTime is 'Unable to verify email because it is in use'
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
FaceTime and iMessage not accepting Apple ID password
FaceTime, Game Center, Messages: Troubleshooting sign in issues
Unable to use FaceTime and iMessage with my apple ID
How to Block Someone on FaceTime
My Facetime Doesn't Ring
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.