It's public garden?? I need to pay for visit this place??

It is part of Central Park. There is no charge.

I have a question, what’s the cost of a photography permit

The Garden is a part of central park. There is no fee to enter this section of the park. A permit is REQUIERD for any photography shoot and a permit must be authorized. The times to the Garden are the Following. November-Febuary: 8am - 5pm March: 8am - 6pm April: 8am - 7pm May - August 14th: 8am - 8pm August 15th: 8am - 7:30pm September: 8am - 7pm October: 8am - 6pm

It is free, it does close at night though.