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The mythological figures are much older than Tolkien, yes, but the representations and standard terminology of most elf/dwarf races are almost exactly derivative of Tolkien. And the answer to your second question is that elves and dwarves will not always do just fine. If there are any significant cultural differences, then you might as well be learning a new race. Besides, I've never found that it takes much work to "learn" a new race. I assume you're refeing to learning the characteristics and history(the latter of which would never be the same anyway). If the author is any good, it takes no work on the readers part at all.
*shrugs* Might just be me. But I tend to get confused with too many new races.
Different tastes, different comfort levels.