Disclaimer: I am not the most experienced at Google AdSense, but I implemented their advertisements on a few websites. What I can tell you is, at least in my case, once you are initially approved to display ads on your first site, it is nearly effortless to display ads on other websites. You do not have to go through a reapplication/verification/etc; you just have to adhere to Google's policies on every website on which you implement the advertisements.
In regards to linuxosr.com, I believe it is just a service, called "Cash Parking," provided by GoDaddy.com to help monetize views while the domain is not in use. It may or may not be subject to the same policies Google places on "real" websites.