I believe I have found a way to do what you are searching for. And I wanted to mention, `timekpr` is still supported, the only issues I had happened when I used the official repository or the .deb files, but when I used a specific PPA I found, it works just fine for me. Anyway, here's the solution.

## Time Limit ##

Install the newer version of `timekpr`:

`sudo add-apt-repository ppa:mjasnik/ppa
sudo apt-get update
sudo apt-get install timekpr`

Once installed, go to the Dash and search for `timekpr` and launch it (all I had to type was "time" until it showed up, so it's not that hard to find). It will ask for the admin password, then you will see various time options, such as saying that "a user can only access a computer for 30 minutes everyday", or you can configure it something like "a user can use this computer anytime between 11:00 AM to 2:00 PM". One thing I do want to mention, however, is that before you change any settings, you must select the option box on the right side of the window (level with the big lock icon) and choose the user you want to configure. 

Once done adjusting those settings, click save, and you will have successfully set up a time limit.


## Web Restrictions ##

I don't think there is a utility that you can use that *doesn't* use DNS or Proxy, but if you are using the firefox browser, the [LeechBlock Addon for Firefox][1] could be helpful, although it would not allow for very flexible restrictions. You can give it a password so that no one else could get into it, and then that user couldn't enter the sites you specify. You could also just restrict whole domains, such as saying that you don't want your cousin to access YouTube because you can't filter it's data, or you can (sometimes) filter sections of websites; for example: suppose a website has an 18+ section, and the link to it was somesite.com/eighteenplus, if you blocked this, nothing on that website that was under the "eighteenplus" folder of the site could be displayed, while at the same time, you could whitelist somesite.com/forkids/ so that the user could access this part freely.


## Application Restrictions ##
See this question: https://askubuntu.com/questions/548568/how-to-block-specific-apps-from-opening-in-specific-accounts

That's pretty much it. Let me know if you have any problems or need any more help.

  [1]: https://addons.mozilla.org/en-US/firefox/addon/leechblock/ "LeechBlock"