This reminds me of an episode of Millenium. The Episode is The Mikado and the killer, The Avatar, kills his victims live on the Internet for the thrill of seeing the hits go up. The hunt is on for the Avatar since he's done this before the Internet came around.

No, you cannot have a site 24/7 that is undetectable. It would take a immense abount of hacking and log hiding with the ISP to do so, and would probably be a full time job maintaining that cover.
I'm surprised no one thought of this: a reverse proxy server. Traditionally proxy server are used by individuals to hid themselves from servers, as a form of privacy. Well the same can be done in reverse: to hid the true source of the server. If you type "Reverse proxy" into google you'll find tonnes of references. As for tracing a person down to their physical address, this gets into the realm of court warrants and such. An ISP will know which subscriber will have what address via their DHCP, but I doubt they'll give it out without a court issued warrant.