I have sampled TdH, EdGB, and EdOV and
1) Gentian root is an alpine flower, the root of which is used in bitters. However, my impression is that in EdGB, the flower is used, and lends a cool light floral note. It has no resemblance whatsoever to vetiver.
2) Only you would know if the seller did you a favor, but my personal opinion is that EdGB is better than EdOV simply because it lasts longer than 30min on me. EdOV smells fantastic coming out of the bottle but I would burn through a 100mL bottle in one week if I wanted to actually smell it. EdGB does a little bit better at 4-6 hours and I think it smells great too.
3) I think there are similarities between EdGB and TdH as well but I get very little of the vetiver in TdH, unlike most people, and don't consider it as much a vetiver scent as a woody. I really like TdH, though, and I think it's better than both EdOV and EdGB. To me, the EdGB is more of a green scent, white musk, a hint of incense; whereas TdH has that citrus opening, flinty notes, and a woody drydown.