1. no Kelvin class did not exist in any TOS books or episodes.. no mention or indication of such.
2. no The name Antares for a starship was first used in the TOS episode "Charlie X", but screen evidence of the vessel is missing and the registry remained unknown .. now if you go by the REMASTERED TOS series - Antares was finally visible in the remastered version of the TOS episode of 2007. The CGI design is a modification of the cargo drone from TAS: "More Tribbles, More Troubles". (quoted from
http://www.ex-astris-scientia.org/articles/antares.htm)
3. no Class III neutron fuel carrier named Kobayashi Maru and even then it is a simualtion ship.. Computer generated, does not exist.
None of these were even created or thought of in the original TOS series.. only created afterwards . The Anteries class was mentioned as the ship in the original "Charlie-X", but the ship's design was never seen.. only "Invented" for the REMASTERED version in 2007.