Not all hosts allow proxies on there servers, you shoudl of checked there TOS first,.
Check the forum here, theres a few out there that will host you..
Nope. Some do while others don't, depending on risks.
One thing you can do is use the search box here for proxy hosts. You'll find a.
Few, I'm sure...
Proxies are very very very resource intensive, nearly every host, especially hosts like http://hostgator.com will suspend your account.
If you're looking to host proxies you're best finding a host specifically for proxy's, such as http://18.104.22.168/~zelune/hosting/..
Proxies can often use HUGE resources. Even a small one with just 100 uniques per day. While it's not illegal to run a proxy what others use the proxy for can be illegal. However that doesn't make you the culprit. Let's say you sell guns...you can't be prosecuted because someone used the gun in a robbery. As long as it's not YOU specifically doing these violations you are in the clear.
I keep a TIGHT reign on them. They need to be checked regularly for bandwidth usage and I have custom tools on proxies to log all activity and I can ban by word, ip, or host. Make sure to also disallow hotlinking. My own proxies actually pay for the entire server.
Proxies CAN make money and lots of it but the reasons you see so many for sale for cheap are for the reasons above. Hosts cancel accounts, admins see the huge resources being sucked away...and they are so easy to setup...
If you are just starting out with proxies: http://www.techentrance.com/proxy-hosting.html is decent.
I would step up to a VPS as fast as possible. Hosteasier.com & fdcservers.net are worth checking out...