I haven't heard of most of those, but Duality is the closed session test server used mainly by the Devs, and Serenity is the Chinese server. Oh and Multiplicity is another test server, but it hasn't been opened up to us for ages.
http://games.chruker.dk/eve_online/server_status.php

China has to have its own server because their govt can't monitor all communications in the game.

No because its a mirror. Its like a parallel version of EvE behind the iron firewall. There is zero interaction between the servers, clients or otherwise. You cannot log onto china eve server without buying a china account and there is some complications with paying for it too, other than that you can play there if you like, but its all in Chinese, Im not sure which Chinese language its in though. There are also restrictions on game times in China, like I think the government cuts you off after 2 hours per day.

I know a few years back the better part of two of the major null sec alliances went to the Chinese server. They had to be very careful about what they said, especially in regard to politics, I think basically the leader where told "welcome, we love that your here but if you act up you risk getting the china server cut off from the outside china. So don't". And by act up they meant; don't mention politics, even as a joke.