You can't play a fae for the simple reason that the fae don't have Free Will. They are creatures driven by compulsion and single minded obsessiveness. If you compelled a fae into doing something in tune with it's nature, it *cannot* refuse. No fate point counter, nothing. This is why the fae are so deeply and even sadistically manipulative ... they're used to driving bargains and creating contracts that cannot be broken, and will always honor a promise ... and will never ever follow the spirit of a contract, but will always follow the it precisely as written and get a good laugh at those who get taken in assuming that spirit of the law and letter of the law are the same thing.
In other words, if you were to play an actual fae, you and the GM would have to come up with one or two Aspects who's compels could never be countered by Fate points. Ever. Ever! Even if it means your enemy finding what your weakness is and then simply exploiting it to your demise.