http://www.windowsphone.com/en-us/ho...-windows-phone This page explains the gist of the My Family feature in WP.
For apps, it logs like you can only allow free and paid, free only, or disallow. You can't set individual apps (which is impossible anyway since there are 275k apps in the store). I think you should just download all apps that you want her to have, then set it to disallow so that any new app installation had to go through you.
As for internet access, anyone can turn on or off Wi-Fi and cellular data since there's no restriction. If you won't have a data plan just turn off cellular data and tell her that she can't use it. As for Wi-Fi, there's no way to restrict it as far as I know. You'll just have to caution her to not connect to suspicious networks.