The casino security tell Nora that counting cards is illegal. It is not illegal federally or in any state in America. Specifically in Atlantic City, the New Jersey Supreme Court has ruled that players cannot be discriminated against (ejected or banned) for counting cards, though the casinos do take counter-measures to try and stop it (like using 8 decks at a time, shuffling at will and moving the cut card near the top of the shoe.) Under no circumstances would it be legal to eject Nora from an Atlantic City casino for counting cards.
Nora meets Melanie outside of Paul's Daughter. That restaurant is in Brooklyn not Atlantic City.