Monitoring child's laptop

This may not fit in the newbie section but I'm still a newbie to Linux so here goes.

I have a laptop running Fedora. I have just bought a replacement and I'd like to pass the laptop to my son for educational use (homework and learning programming) and not to play games (e.g. internet games that don't need to be installed) or use social media.

I would like to be able to do the following:

1. Ensure only a single browser is installed (e.g. Firefox)
2. Ensure the browser can't be used in private mode or allow history to be deleted
3. Disable browser add-ons
4. SSH to check browser history and perform updates/maintenance or install software if he needs it

I'm not sure if 1-3 are possible in Firefox.

It would be nice to be able to perform number 4 (SSH) while I'm away from home so that would need some sort of reverse DNS service and VPN which I don't mind paying for.