2- You are wrong condensation happens because of the temp difference between the glass and ambient air. cold glass, warm and moist air. Both AC and demister fan will demist the glass but blower is faster. The AC drys and cool the the air so equalising temps. The fan blows off the moisture from the glass and the element in the rear screen is a heater As a matter of fact both ac/blower come on same time in the zed and most modern cars when you set the dials to demist function.
The air con lowers the temperature of the air, thus lowering its moisture content(hence condensation from bottom of the car) When the air then heats back up, its ability to hold moisture is improved...
Think of it as a bath, full to the top with water (air 100% saturated), Then lower the bath so water comes out of it (cooling of the air)
Then make the bath back upto its original size, it can now be filled with more water (air less saturated now, so it now has the ability to absorb more water)
sorry its hard to explain without using technical terms, its all to do with the psychrometrics and characteristics of air. Air has a greater ability to hold more water vapour at a higher temperature, dehumidify and then humidify.