Metro connection between Guangzhou South Railway station to Baiyun Intl airport

Hi, is there any metro connection between GZ south Railway station and Baiyun Intl airport? I will arrive around 23:10 at GZ south station from Zhuhai and I have flight at 08:05 in the morning. Please suggest it's my first time there. Suggest the line and stations that I have to cross. Until what time I can get metro at night? I am planing to go straight to airport as soon as I arrived South Railway from Zhuhai. Can I catch metro around 23:30 or after that. what about the taxies avaibility at night time around Railway station? How much the charge to airport? Please suggest.