(1) The answer is "a." There are tons of penniless 21 year-olds. He was just one of many.
(2) This is a bad question. As Mr. Lance said, the answer could be "the" because the sentence refers to a specific niece. On the other hand, there are a lot of Kennedys and they have a lot of kids. By my count, JFK has/had 11 nieces (and I might have missed some. That's a huge family) - so just as she is an (not "a") anchorwoman on tv, she's a niece of the former president.