Q: Why can't I send messages unless iMessage turned on . Works even if not signed in

Take a look at these articles:

If you get an error when trying to activate iMessage or FaceTime - Apple Support

iOS and OS X: Link your phone number and Apple ID for use with FaceTime and iMessage - Apple Support

http://www.igeeksblog.com/fix-imessage-waiting-for-activation/

Try to reset your device. This won't delete your data stored on the phone.

• Press and hold the Sleep/Wake button
• Press and hold on the Home button
• Keep holding both buttons until the display turns off and back on with Apple logo on it.

Alternatively, you may go to Settings - General - Reset - Reset All Settings

https://support.apple.com/en-us/HT201559