Are there transport from Chongqing Airport to the center when arriving at night 1-3 a.m?

Actually, you can still catch the airport shuttle bus, it will keep operating till the last flight ends. And the bus will go to the downtown area, you should get off at Shangqing Temple, which is much nearer the city center.

If take a taxi, it will be CNY 70 – 80 at that time.