"child support" after child moves out

If child has graduated high school and moved out of the house (whether off to college or not), can either parent be required by the other (if divorced) to pay for anything not specifically addressed in an SA?
For example, ex decides that child “needs” a new car, or, to study abroad? What about emergencies, such as medical (if not covered by insurance), or financial (temporary loans, etc.)-- can one ex compel the other to contribute?

No, a parent is not obligated to pay for anything other than what the agreement specifies.