The terms are confusing.
In electronics, a "heat sink" is a device that attaches directly to a component with a temperature problem. Heat transfers from the hot component to the sink by conduction (based on the shared surface area and thermal characteristics). The sink has fins from which the temperature is lost by radiation. There is no liquid exchange.
The devices sold as heat sinks appear to be remote radiators which receive hot ATF from (and return to) the transmission, and cool mostly by convection (air movement due to vehicle speed) and less by radiation. Since many do not have fans and are not located in an air path with a pressure differential, they are less effective.
Some locations may place the sink in hot air from the engine bay, exhaust, water radiator, etc. and do very little. If you're going to use one, I suggest placing a temperature probe in a few places and compare.
Mostly true. The heat sink has fins (i.e. surface area) internally as well as externally. Heat will transfer from the oil into the cooler sink. Heat is then transferred from the sink to air. Very effective at "pulling" heat from the fluid, even if there is no airflow - until it reaches near or the same temp as the oil. However, airflow will help, obviously, so a fan is a plus. I put them under the car away from exhaust/engine heat as much as possible. Being able to take it apart and clean it is a big plus for me using one.
Again, not for a street car, tow truck, etc.
