In New York State (Queens County) does child support cover things like swimming, acting or martial arts classes?

A child support clause in a divorce agreement will usually have a provision for splitting payment of the expense of the child's activities, college, religious school, etc, depending on the family.  In a contested divorce a court might order one party to pay, or order both parents to split expenses. The bottom line is that the law sees value in children participating in activities such as you describe, and unless the custodial parent enrolls the child in activities that are way beyond the finances of the other parent, both parents will usually have to contribute.