No - ceiling fans require UL-listed fan-rated metal boxes with special bracing that can support at least 50 lbs dynamic weight.

Remove the cover, vacuum dust, wipe blades with soapy water, and clear exterior vent flaps.

Consider CFM (cubic feet per minute) rating (1 CFM per sq. ft. of bathroom size), noise level (sones), and features like humidity sensors or built-in lighting.