1) If vWLC was down. Are 3 AccessPoint still working without controller?
I am going to presume you only have ONE controller.
If you have FlexConnect running AND the APs did not REBOOT, then the APs will be able to work. If you have a local authentication server at the site, the AP will be able to serve new authentication whilst the connection from the AP to the vWLC is still down. Just make sure you DO NOT REBOOT the AP.
2) I can't understand FlexConnect clearly. Is there any help in this situation?
Wireless BYOD for FlexConnect Deployment Guide