-No, it is counted from the date (1/20/2010) that USCIS request you to leave after your F1 application was denial.
2. I suspect denial was due to OOS after layoff before filing for I-539 - RFE was evidence on payroll between 7/20/09 to 8/1/09. I will update once I get the letter.
-Then, it is most likely that reason.
3. I probably will need to go back to Singapore to apply for F-1. How would my OOS affect my F-1 application?
-You just go to Singapore to apply for the F1 visa and I believe you should have no problem to get it.