In practice the answer is effectively yes. Technically they may call it something else ("detained", perhaps), but there's no fundamental reason that a police officer anywhere cannot take a child into custody if the police officer believes that that child has committed a crime.
child support stops at age 21 in NY
21
18.
No
age 21 see link below
14
see related question
18
Child labor laws allow a person to take a job at 16.
No, for example in NY, the dropout age is 16.
16. a child can quit school at 16 in ny
yes