Подарок means 'gift' in the sense of 'present'. It's usually a physical object indeed, but can be used in a sense of 'gift' in other cases as well - for example, something like "that back-pass was a gift for the striker, what an amateur mistake in defence" would translate directly into Russian, using 'подарок'. It's quite often used ironically, ...
Подарок has got a figurative meaning in Russian, when we mention something causing great pleasure.
Ваш приход - большой подарок для меня.
Такая хорошая погода — просто подарок!
Его приезд — настоящий подарок. Подарок судьбы.
We can also use не подарок in the negative sense, describing people , who are not quite pleasant to communicate or to deal with.
Он не ...
I didn't expect I would feel this
If you are looking for a way to convey a surge of emotion you wouldn't expect to feel before, I would go with что-то:
— Это, Боб, такое дело, Мэллори сегодня и правда выиграл в лотерею миллион долларов!
— Ну вот. Теперь мне что-то завидно.
Что-то particularly conveys that you didn't not expect you would feel envious but ...
A gift is a "подарок" in Russian if we can identify the act of giving
"Подарок" is indeed typically a physical present, but it also can be an abstract, figurative thing - if we can say that there was a moment when the recipient got this gift. In this sense, talents and other innate gifts from God/nature are not "подарки" because ...
You are right a talent is not something you work for it is something you are born with. Doesn't "gift" have the same connotation as "дар", as something innate? If not then maybe "endowed" would be a better analogue here (as compared to "одарённый"). In any case all these words have the same root, "дар".