katzglobal.com doesn't ask for your address when you register a domain name, sites like torrenthound(.)com use it. lets you pay by cash in post.
server; well, you have three options as far as I see it (ones illegal, other two are legal).
server op 1;
steal credit card, fraud -- pay server that way -- if they found out your server would be suspended *educational purpose, i don't recommend it since I hate frauderers
server op 2;
make an infinate loop of money (make the server self pay itself)... example, make payment subscription with a payment gateway (for this i'll use paypal as an example) get an ad network to pay money into it... as long as you keep on earning more than server fees you'll be fine (to get the first payment into your paypal so you can get bigger servers etc you need to start on a free web host and build up ad revenue .. get bigger paid hosting etc).
server op 3;
services like prq.se, lets you pay via cash in post rather than credit card.
hide ip with vpn ... or even free wifi hotspot ... make sure you use a mac address spoofer.
^ quickly wrote it so may not have thought about some things.
... tbh, paying for a server / domain name you can use your own credit card and real info ... you just have to trust them with your privacy (will they release you info?) ... this way is a big of a gamble, ad networks and fb profiles are the way most people can find out the original owner since offshore hosting normally keeps your info safe.