Is there a way to lock the volume & brightness on iPad/iOS 10 from getting changed by a child?
For brightness, you can go in Settings > Control Center and change if you want access to Control Center on the lock screen or within apps, it will always be available on the home screen, AFAIK.

To prevent him from changing the volume, change the volume to what you always want it to be and go to Settings > General > Restrictions and tap Enable Restrictions, then set a Restrictions passcode (something different than the normal passcode). Go to Volume Limit and check Don't Allow Changes.