Serenity and Tranquility are the only live Eve servers which have existed. Anything else is development.
Korea didn’t get their own server, they just got a translated version of the client, to make it easier for those koreans who don’t speak, or are not comfortable playing in, English.
Currently, Serenity isn’t running, because of issues with the Chinese government. All games in China require approval by their government, and this has not been forthcoming yet. There’s a closed beta, but that’s it. It had been running with one partner, and CCP decided not to renew with them, moving to another partner. CCP can’t run the game themselves in China. If/When approval is forthcoming, Serenity will properly reopen.
Those Chinese citizens playing on TQ are doing so in violation of their country’s laws (as far as I understand it. I’m not a lawyer)