Selective Background Updating in Running Gaussian Average Method for Background Subtraction
1) You start with first frame of video. Gather several frames to calculate accumulators, denote everything like background - at first frame you do not know which is which. Yes, recalculate.

2) Yes we shall update variance. 

Never used unmodifief version: remember to use illumination infependent color space. Think about taking running variance on your own.