Should this be "the history" in the sense of the history of a particular thing, or "history" in the sense of the general study of the past?
It should be "the history", as "history" as a general study of the past would be "geschiedenis" (whithout 'de' (so whithout lidwoord (article)))
Why doesn't history end with "kunde" like all the other subjects?
Good question. Old word that's just not used anymore. -kunde is just easier I guess.
Geschiedkunde also exists, but isn't used much. The adjective, geschiedkundige, is less uncommon.