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.
Did you ever get an answer? I am wondering the same thing. I have a Mini iPad and using an Apple Wireless Keyboard but cannot get any config to Send a text unless I reach up and touch the screen send button. Which is ridiculous to have to do. Sorry Texas Mac Man, none of your answers or links addressed the question of how to "hit Send" using an Apple Wireless Keyboard.
This does seem like a huge oversight, and I've been scouring the web myself for an answer. But the main answer seems to be NO - you cannot simply hit enter after typing in some text in Messenger to send the message.
Oddly enough, this is just a simple app problem, not an iPad problem. When I use Skype instead of Messenger, the return key on my wireless bluetooth keyboard is mapped to the send button, so I can rapidly type away, hit enter, and type away some more, without having to lift a finger to each over and hit the send button.
I just now submitted some feedback to Apple, but after my web searches, it appears this has been a requested feature for awhile, so who knows when we will finally see it actualized.
If I ever do find a solution, I'll let you know!