I'm having the same trouble understanding that sentence as you do. Since we can't change the main sentences and only the translations, I feel like I should at least add "the kinds of myth" as a translation to "Τα είδη του μύθου", no?
Yes, that's an accepted translation. The translation here does match the sentence exactly, which is a bit odd. But, it's not too much of a catastrophy, since that alternative is included as well. ^.^
No. τους μύθους is the accusative case -- your phrase would mean "the kinds the myths", more or less. Just two unrelated noun phrases next to each other, not connected at all.