The remote control sends a radio signal to the base unit, and the base unit interprets the signal to switch the connected appliance on or off. Some remote control can operate multiple switches from a distance.
Yes, in fact my ceiling fan and light are controlled by remote control, mine is made by designe control (DC)
They both use an "RF" control, something similar to an SOS signal on a boat.
eBay or an RC store
buy a universal control
a control switch is a sort of remote controlled relay attached to home appliances which consumes more power.