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Yes the Switch Hosting (Plastic) can leak due to Heat over the years.. Just replacing the switch can help it a lot..
You probably have a leak in the heater core.
With no water no heat can be transferred through the heater coils.
Any capacitor will leak some of its energy, because there is no such thing as a perfect insulator. All materials have some conductivity.
No.
The car will over heat.
Coolant leak, possible heater core. Suggest to have it pressure tested to find leak.
Likely an exhaust leak
Drive it high speed two miles to get it up to operating heat. Stop and raise the hood and look for the leak. Have a flashlight too. When the vehicle stops the engine will super heat the water and the leak will show itself. Be carefull - it can be violent. If the interior smells sweet you may have a leak in the heater core. LoL
Plumbers have tools to help them find leaks. Putting air pressure through the pipes can help them to find a leak in the wall.
Either you can have a leak from the internal venting system that is causing this or you have a leaking heater core instead.............
A small leak in a head gasket. When the engine is hot the head expands and the leak opens up. When the cooling fan comes on it removes some of the heat and the leak closes back up. This will not last, the leak will get bigger and leak all the time.