first thing you need to confirm is that the car has coolant in it. the spill over you showed in the picture looks like a green coolant which is not of good quality or very old.
2ndly i think your thermostat valve needs to be checked in case both fans are running.
by the way the fan on the driver side is condensor/AC fan and it should run with AC.
the fan on the front passenger side is the radiator fan and it runs when the car needs cooling. once the radiator fan runs the thermostat valve opens and allow water into the cooling path of engine to absorb the heat.
you get to know regarding waterbody functionality by observing. if there is some hissing sound from the driver side of the engine once the radiator fan is running than it means that waterbody might be making a noise which it shouldnt. if there is no such sound you are good.
which city r u in?