While you can't really turn them off, you can make it require a PIN to make said purchases.
1. Tap the "Google Play Store" app and then tap the "Menu" on the upper left.
2. Scroll down and tap "Settings".
3. In here scroll to "require authentication for purchases (or however named on your device).
4. Then choose how you want to set it from the options listed.
5. You may also want to set the"Parental Controls" as well.
This, however, won't stop all your problems. While it may stop the purchase of apps or the viewing/obtaining of apps not appropriate for the age you set, it won't stop a lot of other things from possibly going wrong. I would suggest you set the device to not have WiFi or data access. Just 'forget' the password for your...