In my Russian class, we are learning holiday vocabulary, and I am wondering if there exists an abstract meaning for “подарок». For example, could you be talking about “the gift of forgiveness” or “the gift of gab” or a “gifted pianist”? Or is подарок limited to a physical present you can see?
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, when someone inadvertently helps someone they really shouldn't have. Also when something unexpectedly good happens you can use 'подарок', so it doesn't have to be a Christmas or Birthday or whatever present.
'Gift' in the sense of 'talent' in Russian is 'дар'. 'He/she 's got a gift' - would be 'у него/неё - дар [от бога/от природы]'. Дар can also be used for 'present', but it sounds rather archaic or even overly pompous when used in that sense (unless you're being ironic or facetious). It's used in legalese (when you 'gift' a property, for example) and you come across that usage in many quotations and expressions. So in general it can also mean a physical gift, but it's not common in every day colloquial speech.
And 'даром' means 'free', as in free of charge.
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 подарок. Такая тёща — не подарок. Ребёнок попался хоть и пятилетний, но далеко не подарок.
We use дар and талант about abilities, which is covered in the previous answer.
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".
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 a person was born with it rather than acquired it at a later time.
But if something was clearly bestowed after someone was born, then the word "подарок" is appropriate. Phraseme "подарок судьбы" is often used in this context.