"You are an American boy."
Translation:Tu es un garçon américain.
"Vous êtes un garçon américain" is correct, because "vous" is in the polite singular form.
Yes, in particular if you don't know and that you feel that he expects to be treated as an adult and not as a child.
I also made the mistake of assuming that the Tu form was the only correct answer, but apparently some figures of authority such as police may use vous to talk to singular children as a sign of formality.
We capitalize proper nouns, not adjectives: je suis français - je suis un Français.