To the OP:
“There is a new amusement place in the Palisades Center named Fun City. They have an add in the local Monsey add paper that the pizza there is Cholov Yisroel and Pas Yisroel under the supervision of Rav Asher Schechter.”
Please reread the ad, and then reread your opening statement. Does the ad claim the pizza is under the hecsher of Rav Schechter or does the ad state they have a kosher concession stand that sells kosher pizza that is pas yisroel and that the concession stand is under the supervision of Rav Schechter. It should not take a Pinkerton detective to figure this out.
Then, please answer if the KOSHER concession stand is open on shabbos, OR is Fun City open for business on shabbos and selling concessions from its NON Kosher concession stand where no kashrus claims are made. If the KOSHER concession stand is open on shabbos, please tell us how you know this?