So if I don’t have a permit to park here where do I park ? Are there private parking lots so I can leave the car and pay per hour or so?

There is nowhere to park without a permit and you can't pay per hour. If you leave your car in the parking lot you will get a ticket. Even if it's empty.

This year they are not selling day passes nor permits to non-residents and all the nearby streets have No parking, standing, stopping signs.

i think that long island loose a lot of visitors from ny because there are no parking spots for visitors