Unless in use, doors should remain closed as much as possible to avoid disturbing the planned air volume, circulation, and temperature. There is no hall on the south side of level one. This does not affect circulation because the ventilation system for that area is designed to handle the full dimensions of the room. The system normally has outside air at all times, as explained in question 3 above. Butler is not a sealed building.
Air is heated and cooled at a central air handler in the basement.
Basically hot water and chilled water pass through separate coils at the air handler. As the air passes over each coil it is heated or chilled to the required temperature. The coils have control valves which introduce the appropriate medium to the coils to control the discharge temperature from the air handler. The discharge temperature is controlled by the current temperature of the space and the desired temperature. If the space temperature is too high, then the heating control valve closes down and the chilled water control valve opens more.