Many people insist that 'the first black president' is actually not black.
It goes on to discuss the fact that people sometimes view people of mixed races differently, which I don't think is a surprise. But nonetheless, it's a pretty interesting article, and it casts some light on the above questions. Personally, I find it intriguing that just based on a person's actions, they can choose their identity if they are of mixed race.
It reminds me of a great short essay by David Matthews from the NYT a couple years ago. Ultimately, according to him, racial identification can come down to a choice.