The dialogue in "Obsession" specifically says, twice, that the creature attacked the
Farragut -- the ship, not just the crew. So despite what the Shatnerverse novel portrayed, it's probable the incident was in space.
The class of the
Farragut wasn't established canonically, but tie-ins and references assumed it was
Constitution-class. However, the
Farragut was apparently one of the ships in the Vulcan rescue fleet seen in the 2009 movie, so if that was the same ship (which it could've been if it was built before 2233), then it presumably would've been one of the "guest" ship classes seen in that fleet.
But
Josan's right -- "Obsession" does say both that half the crew was killed and that 200 people were killed, so it was probably a class similar in size to the (Prime-universe)
Constitution class.
I figure Kirk probably went through a variety of stations as part of his command-track training, much as Chekov went from science to navigation to security (and according to a theory from DC Comics'
Who's Who in Star Trek, started out in engineering, which is where Khan met him during "Space Seed"). Tactical may have been one of his posts, but I think he occasionally showed some ability to help out in engineering.
I believe you are correct. Memory Alpha says he started out as the flight controller, aka conn officer, on the Stargazer. Doesn't say where the info comes from, though.
Whoever wrote that entry might be misinterpreting a line from "The Battle" where Picard said he remembered "being at the helm of the
Stargazer" at Maxia Zeta -- which in that context would have to mean "at the helm" in the sense of "in command."