One good thing about Forbidden Zones? Outside laws didn't apply here. That's not to say there weren't any laws - killing residents was frowned upon, unless it happened in a fight between two (or more) willing participants, and stealing was also outlawed. The city wouldn't be able to function as well as it did if the people were just left to do whatever they wanted. There was a group belonging to the secret organization, dedicated to maintaining peace, so that businesses could function, and people could still live their lives - perhaps not normal by the outside standards, but no one who came to a Forbidden Zone expected that.
There wasn't any rule forbidding the use of abilities, though. Every Esper just used their abilities as they pleased, and it was only when they did something they shouldn't have with them that they were punished for it.