B737 Recirculation Fans.
 

During various phases, of flight, these Fans turn OFF and come back ON, automatically? Why?

Huh? Normally they don't! They both (unless there only is one like on the -700) always operate unless someone (hopefully not to have a smoke in the cockpit :=) set a pack to high flow or turned them off manually. Do you have a concrete example?

Are you getting a flight deck warning/alert that this is happening?

Often the fwd galley ovens sound like a major rotating assembly running down when their fans switch off!

If you are detecting such an audio cue, next time phone cc and check with them regarding oven use. :)