It seems to me that a more proper English sentence would be "I would have been an elf, if I could have chosen myself." It feels wrong without that parallel construction.

There is a mistake in the "correct" solution: I entered "a pixie" but Duolingo highlighted this as a mistake and showed this solution instead: "I would have been an pixie, if I could choose myself." It should definitely NOT be "an pixie".

Why is it wrong to put: 'I would have been an elf, if I myself could choose." ?

Can a native speaker confirm that the tenses in Danish are correct?