1. I would strongly suggest to pick up your bags at SFO and recheck them with SQ. I doubt that SOuthwest will trhough-check to SIN, while SQ is likely to do it, especially for a F class pax. That will also reduce the risk of getting the bag stranded at SFO.

2. Do OLCI for KA before leaving (48 hours). Make sure that you bring the BP and a copy of the KKG-KHH ticket when you checkin at SFO on SQ.

3. AT HKG you will only need to go through security. Might be a good idea to ask the KA agent if your bag is loaded on the flight. If not, they will retag.