Yes, as a 1K it should be no problem to make changes to awards, assuming the seats open up.

There is currently no nonstop SFO-SIN, so assuming you are on the nonstop LAX-SIN, you would not really be saving too much time. If you did SFO direct you would have to stop in either ICN or HKG. Chances of seats opening up really vary. It is not unusual at all for SQ to open up plenty of C and F seats prior to departure, but typically only a few days ahead of time. There is no time or dates that I have noticed for awards appearing.