we are going from chongquing to hong kong, is it possible and what are the fares? thanks

yes, it is possible, but there is no direct rail service.
you can get to shenzhen on a 33 hour overnight rail trip, and then pass the immigration and customs check at any port and you will reach Hong Kong.
Alternatively, you can travel from Chongqing to Shanghai by high-speed rail, and then the through train from shanghai to Hongkong.