I am currently using: 1And1 Name.com They are both very good and the support is also very good in case you need it. Out of the 2 I prefer Name.com since the DNS changes happen faster.
Why not just change the whois information afterwards to something fake? I don't like suggesting that but you have no idea how often I see whois like that.
You cannot do that. Read the ICANN rules. Soon or later the registrar can shutdown the domain if they find false information in the domain administration info.
At GoDots.net every domain comes with free private protection feature. And the domains are cheap too.
I've very familiar with the ICANN rules, trust me. In over 26 years on the net, I've seen them go after a total of *1* domain with false information. Granted there's been a couple of reports that GoDaddy is starting to go after folks. Then you have the http://rfc-ignorant.org folks as well although not many people listen to him. Never said it was a good idea, just that it was done.