Teamviewer allows you to peak in anytime, to see what they are doing. But really if you want to know what he is doing, just ask him for the computer, and go through his history and you can also go through the router logs. You are the parent, you own him until he leaves your home. If he does not want to comply, then unhook the computer from the router, and place a lock on the case, along with those ports like the USB & Ethernet, which you can purchase online, to keep him from attaching back to the wired network, or attempting to use a USB device to go online.
Also if you are wanting to be the parent, use Parental Controls or as it is now know on Windows 8, Family Safety. Set him up under your account as a child. You can also make him as a limited user, and you as the administrator, so that he cannot create any accounts, only you can. If you really want to harden the system and the computer is not running Windows 8.1 Pro, I highly suggest purchasing a Pro license, so you can tighten the policies on the machine.
Your router log will tell you more then he realizes, in where he is going and what he is doing. You can also roll your own router with either pfSense, Smoothwall, or use a Business or Enterprise router, that you can have better control, or use a router that you can load DD-WRT, OpenWRT or Tomato on.
I have an old buddy that owns a business that sells keyloggers, but they are mostly USB style, but he also has some "Man in the middle" type.