We will appreciate your support clarifying the following points:
1-False air effect upon the (increase/decrease) of dust load in a closed system of air swept type ball mill (between the mill outlet duct-separator-cyclones-filter-stack). Also, will the dust resistivity increase/decrease?

In an air-swept mill false air is usually introduced at the bottom of the ascension pipe in order to ensure there is sufficient volume, density and velocity of air to lift the ground material up the ascension pipe and through the separator. The amount of dust being carried up the ascension pipe is the same, however the volume of air is greater therefore the overall effect is a dilution of the dust load. In principle the false air will cause a reduction of the temperature and this will reduce the resistivity of the dust improving the electrostatic precipitation.

I own a 400tpd cement plant. Because of a recent reshuffle in government, the state is now asking us prove our pollution-free state of running. How can I prove the technology is a pollution-free one.

You need to begin the process of obtaining ISO 14001 certification for environmental management systems. There are various consulting companies who should be able to help you with this process.