Hi there, DaveD7.
Thanks for using Apple Support Communities! It appears you're not receiving the "Ask to Buy" notifications from your son's requests for the additional levels in Super Mario Run. But, when he checks the status, it's showing he can only proceed once you've approved. I use Family Sharing with my son too and I'll be glad to help.
Get help using Ask to Buy -- Check yours and your son's settings to make sure you're being notified as you should.
Let me know how that goes and take care!