Does turning on the heat waste gas?

no it does not waste gas

and yes! if your car starts getting too hot turn on your heater full blast. what that does is relieves the car of the excess heat. so if that ever happens you need to turn on your heater and you can pull over with it on until it gets to a cooler temp or keep driving if you have to and you notice that it is then going down not up.

As this is related to automotive,..... absolutely not. In fact: opening up the vacuum door that allows heat to be pulled from the heater core helps out the cooling of the engine. No down side there.

The only mode of heat that does slightly use more fuel is the defrost, where the compressor is engaged in order to dry the heat.

It doesn't waste it, it uses it and you get warm in return.

As for the car, turning on the heat does add a few square inches of radiator surface area by way of the heater core. But that's extremely minimal and if your car is overheating it has another issue that needs addressed.

The heat comes from the coolant system, and the coolant would still be hot with the heater turned to cold. So, it does not use more gas.

Yes running heat , waste gas depending on what type of car/truck you have.