There might not be anything that does all of this at once, but a couple of programs combined might do the trick.
If you just want to block inappropriate websites from his searches then you could adjust the Google search settings. There is this thing called "SafeSearch" on Google (you've probably used it before) where you can set the protection settings to "Moderate" or "Strict" or you can turn them off. This is a part of Google so you don't have to download anything...you just have to press a button. You can also block any websites with specific words from the search. So say you wanted to keep him off Facebook then you could block the word "Facebook," and he wouldn't be able to access it. There's a bit of a glitch with this because if you block something like Facebook then all websites (even academic ones) that are connected to Facebook will be blocked. Even websites that enable users to comment and have Facebook mentioned in the comment will be blocked. So if you have him using the computer for academic purposes it might impair his research. Also as far as I know whoever is using the computer can change the Google search settings and there isn't a way to prevent them from doing so (so if he figured out how to change them you might be in trouble) and those search settings only apply to Google so if he decided to use Bing he'd still be able to search whatever he wanted.
It might be good as an extra precaution though. So here's the informational website:
http://support.google.com/websearch/bin/answer.py?hl=en&answer=2519950&rd=1
As for turning the computer off its kind of primitive, but what I would do is take the battery out and then have him plug it into a timed power strip that turns off at 10:00 PM. So that way the computer won't keep going on battery power and the power will turn off at 10:00 PM so there's no way for him to continue using it. Of course he still could plug it into another outlet.
You could also have him unplug the computer at 8:00 PM so by 10:00 PM it will die.
Okay, wait. I just found a website that explains how to shut it down on a PC. You don't have to download anything...it's just something funky that you do with the settings, but it does work because I just tried it. If you have a Mac then all you also have to adjust your settings.
http://answers.microsoft.com/en-us/windows/forum/windows_7-performance/how-to-schedule-computer-to-shut-down-at-a-certain/800ed207-f630-480d-8c92-dff2313c193b
One more thing. In addition to all that I found a parental control program which allows you to block sites yourself, protects from inappropriate content, allows you to set up time quotas, and sends you email alerts whenever you're kid types in a phrase that's inappropriate or receives a phrase on chat that's inappropriate. It actually sound fabulous.
Here it is:
http://www.kidswatch.com/
However, if your son is older then you might not want to take all these measures because it's a bit of an invasion of privacy. Monitoring his personal messages seems a bit extreme, but there are still some fantastic features on this the program. So it's something to consider.
The best of luck!