I will arrive to Baiyun Airports at 3 am. Does the subway still open at this time?

I’m afraid the subway will not work at that time. You can take the Airport Express Line 5 to Haizhu Square Station. Upon arrival, you need to walk westwards along the Yide Road for around 120 yards (110 meters) and turn right to South Jiefang Road for 460 yards (420 meters). Then you may turn left to Dade Road for about 130 yards (120 meters) to your hotel. This airport express operates till to the last flight arrival. The ticket fare is CNY21/person.