A proxy site masks your IP address by redirecting traffic.It is illegal because it masks your identity
I started a proxy with no help and it was successful. I know run several that make me a fair few pennies To assassin. They are ileagle in certain countries like china.
Trying to explain logic to illogical people is a waste of time. They are not illegal. I run dozens of proxy websites and anyone just starting now will find it very hard to make a profit. You will make a nice return in the first couple days but when smart pricing kicks in you will find it hard. The fact that you need at least a powerful VPN to run effectively makes a bit of investment necessary aswell. Just as an example of how difficult it is at the moment. I saw proxy.org lose almost 10,000 listed proxies in the last couple weeks.
Huge Guide on Promoting and Optimizing AdSense on Proxy Sites http://forums.digitalpoint.com/showthread.php?t=197274