If you use an evaporator tower you do need to replenish that water. The tower is usually used to cool a closed loop of water (or glycol/water mix depending on the climate) that cools the refrigerant in a chiller.

The system in the article uses a pipe loop underground in place of an evaporator. This uses less water/energy but require a higher first cost and very specific location requirements which is why the cooling towers are still more popular.

They are definitely not closed; poorly maintained, the water vapor they output can spread pathogens for miles. Cooling towers were blamed for the recent outbreak of Legionnaires' disease in New York City.

I wouldn't doubt it. Even a small domestic AC can be mold city if not cleaned regularly. It's a warm and moist environment just perfect for all types of bugs.

It depends and yes.

Some systems will have a closed system using water or ammonia as the intermediary medium. The coolant is pumped to an air handler on each floor where it cools a condenser filled with refrigerant.

Most chillers are just a big empty box where water is poured over the coils. The evaporating effect cools the medium inside and vents as steam or water vapour.

"Chillers" are actually direct expansion cooling devices for liquid. They have a condenser and evaporator just like an air cooled air conditioning system. The evaporator will be on the chilled water supply side and the condenser can be cooled by water or air.

The big empty box with water is an evaporative cooling tower used to cool the condenser side water.