Has he searched for the pictures yet using a file explorer like Solid Explorer? They're usually in the DCIM folder in internal storage.
Solid Explorer: https://play.google.com/store/apps/details?id=pl.solidexplorer
I'd still recommend using a file explorer from the Play Store to try to locate them. If that doesn't work, try using a data recovery tool like this one:
https://play.google.com/store/apps/details?id=com.baloota.dumpster
Based on my own experience, I suppose iKeyMonitor Android parental control app is good. It supports the logging of keystrokes, call recording, capturing screenshots. Besides that, it also provides many other parental features.
You could try google's Datally.
Blurb: >DATA SAVER - Save mobile data by blocking background data and unwanted notifications. You can block background data for some apps and allow for others.
I'm not sure you could lock it down such that your kid can't turn it off, though. If you can limit it at the carriers side, say allocation - 50 MB then if you need to "find" him you'd just login to the carrier control panel and bump it back up + 50 and use whatever locator software.
I HIGHLY recommend Join by the same Dev who owns Tasker. I've tried AirDroid, pushbullet, Cortana even my own Tasker design and nothing has been as good as join. I will link it below https://play.google.com/store/apps/details?id=com.joaomgcd.join
The only app I could think of that would be any help would be SlideBox, which is more of an organizer app for already taken pictures. It will create new folders and store the pictures in those folders as he selects them, but this requires him to switch between his camera app and SlideBox before moving to the next room.