Unable to send messages and access Mail on child's iPad

I'm having issues with how I'm setting my kid's iPad.

Basically, they want to message their friends. They have their own iPad, which is setup with a kid's account and I'm the parent account holder. I tried to message myself right after setup by entering my phone number or my e-mail, no dice. When I tried to send a message via my phone number (I have an iPhone), it just turns red and the blue button becomes dim and disabled. When I tried to enter my e-mail address in order to send messages to myself, every message that I tried to send did not work and I got a message saying "Not Delivered".

I then tried to setup e-mail (they have gmail), but hit a snag there as well. I added their gmail account (which is also a child's e-mail account) and when I try to use it to load their e-mails (not that many), it doesn't load, I see an "Account Error: xyxyxyxyxyx@gmail.com Details..." and when I click on "Details...", I see a pop-up saying "xyxyxyxyxyx@gmail.com is currently unavailable". Now I'm very confused. I know I can get into that account via my laptop's browser... what is it that's not available?

Look, I want to give my kid the ability to message their friends and e-mail, that's it. How do I do that?