I'm not sure on TS places. I've heard that the non-Disney owned and operated ones can be strict, while I think the Disney owned and operated ones are more lenient. Someone else may be able to chime in here.
As far as counter service, anyone can order anything they want. I've ordered kid's meals several times, mostly because the adult portion is entirely too much food for any reasonable person to eat (except perhaps a teenage boy).
At buffets and AYCTE places, everyone over 9 pays the adult price, no exceptions.