Ethnicity is a different thing than gender. Ethnicity is part of your family's lineage - for example, African Americans have roots in African people. I'll volunteer myself as an example. I am Caucasian, and my family tree goes back to Poland, Canada, Ireland, etc. Does my family roots mean anything? Only that my family lived in those countries and have been predominantly white. Somewhat - knowing where your family originates tends to help you track how the family has changed over the years, but that has a flaw. I've seen people go off about being Native American when that branch of the family is pretty distant. There was a lady up here running for Senate, Elizabeth Warren, who clained to be 1/16th Native American. It is part of her heritage - nothing special - but she was trying to use it as a sort of selling point.
As for the lady you posted - She can't identify as African American because of her family's lineage. Unless she can produce documents proving there was an African American in her family tree somewhere, it holds no ground. Heritage is a completely different thing from gender identity - one is primarily in the genes (ethnicity) and one is mental (gender).
Note: Please do not bring race into a discussion about gender. It's a can of worms best left sealed.
For the age thing:
You can feel older or younger, but legal documents such as a license, birth certificate, etc. are there to keep people from doing that - there would be a hell of a lot of legal issues surrounding sexual reproduction (Age of consent), cigarettes, alcohol, eligibility to drive, access to gentlemen's clubs, bars, nightclubs...I can't think of anything else.
Your questions are falling a bit too close to the article I previously commented against.
I never mentioned "transgendered". I have transgender friends who would get super-pissed if I ever said that. Thanks for the clarification.