Why would they send Duncan to a juvenile correctional facility if he messed up at the group home?? Do they think he was in the wrong?

Short answer: they wouldn't. Duncan, in his state of anxiety, is oblivious to much of the conversation that takes place between the social worker and Mrs. Brush. Being placed in a correctional facility is the last option, but Duncan focuses on this as the only other option besides being sent back with Bruce because he is so desperate to get out of the situation he is in.

Is he Anorexic?

Duncan isn't consciously anorexic, but he does tend to skip a lot of meals. His main focus so far in life has been avoiding Bruce's treatment, and food is often far from his mind. Also, Duncan has found that when he eats and then is thrown into an extremely stressful situation, he throws up whatever is in his stomach. From Duncan's point of view, hunger is not important, and his stress levels make it difficult to eat and keep anything down if he does eat anything.