🪭What size ceiling fan does this room need?

144 sq ft, so a 44-inch fan — right at the top of that band. A 52-inch would also work and would move more air at a lower speed, which is quieter; the limit is that blades need at least 18 inches of clearance from every wall, so measure before going up a size.

No — it cools people. The air movement speeds evaporation from skin, which feels roughly 4 °F cooler without changing the air temperature at all. That is why leaving a fan on in an empty room does nothing except add the motor’s heat, and why the fan and the air conditioner together let you set the thermostat higher.

Counter-clockwise seen from below, so it pushes air straight down and you feel the draught. In winter, reverse it to clockwise on the lowest speed: it pulls air up the middle and pushes the warm air that has collected at the ceiling gently down the walls, without a draught. That switch is on the motor housing and almost nobody uses it.

Eight to nine feet above the floor for the best airflow, with a minimum of seven feet for safety. On a standard eight-foot ceiling that means a flush or low-profile mount; on a nine or ten-foot ceiling a downrod brings it into the right band. Sloped ceilings need an angled mount and a longer rod so the blades stay level and clear.

Two, once a room is longer than about 18 feet. A single fan produces a column of moving air roughly its own diameter plus a margin, so one 60-inch fan in a 24-foot room leaves both ends still. Two 44-inch fans spaced along the room cover it, run slower and are quieter.

Not by themselves. Airflow comes from blade pitch, motor speed and span; blade count mostly changes noise and looks. A well-pitched three-blade fan commonly moves more air than a flat-bladed five. The number to compare is CFM at high speed, which manufacturers publish, rather than the blade count.