Fly from Singapore to HKIA to take ferry to Zhongshan. What do i do with the checked in baggage?

You can take the ferry from Skypier in HKIA to Zhongshan. However, you don't need to collect the luggage at HKIA. Upon landing, just go to the E2 CKS Service Counter of Zhujiang Passenger Transport. The detailed English signs at HKIA will help you a lot. Don't worry. Your luggage can be delivered to the destination directly.