Can I still add friends to Game Center on iOS 9? My iPhone and my daughter's iPod both have iOS 9. I have tried to add her as a friend in Game Center using both her email address and her nickname. But nothing seems to work.

She has also sent a request to me. But nothing seems to get through.

I have read that game center does not allow adding friends in iOS 10. Does that mean it also doesn't work I iOS 9 now? 

Note: my daughter is under 13 and we have entered her age as such. That does kind of limitations in some games. But I had not heard that it would block her from using Game Center friends.
Many Game Center's features were removed from the Game Center service itself so they still wouldn't work, including adding friends, even if you have Ios 9 (and in Ios 10 obviously).
Now, you  can see just the rankings and the goals of the game; you can also invite and challenge your friends only through iMessage, and only if the game supports it.