The only theme parks that have a no fly zones are Disney's. You can't fly within 3 miles nor lower than 3000ft. They got those passed right after 9/11. But Disney wants that adjusted, as the law prohibits drones...and Disney wants to do drone displays (Universal had dinner at least one).
For the rest of the parks FAA regulations state -
Over congested areas – Over any congested area of a city, town, or settlement, or over any open-air assembly of persons, an altitude of 1,000 feet above the highest obstacle within a horizontal radius of 2,000 feet of the aircraft.
As I've read flying drones "over people" requires special waivers.
And, yes, Chopper 10 still exists.
Edit- Speaking of helicopters, the FAA says - Helicopters may be operated at less than the minimums prescribed In
paragraph (b) or (c) of this section if the operation is conducted without hazard to persons or property on the surface.