Engine

You have to actually look at it. Can't tell over a computer. The fact you didn't smell anything after one of the restarts suggests it is a slow leak and the coolant boiled off previously. Some of the possibilities are a corroded head gasket, rusted off heater hose clamp, leaking heater hose, corroded engine block core plug, leaking water pump, or a leaking heater core. Only the head gasket is relatively serious but the heater core can be rather time-consuming.

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Nope. If the thermostat sticks open, the heater will blow cold air and the engine will not get up to normal operating temperature. If it sticks closed, the engine will overheat and you could see or hear coolant boiling into the reservoir. You might smell that but it usually won't be smoking, at least not from the back of the engine.

There are a few things that can be tested. First, a cooling system pressure tester can be used to pressurize the system, then you can look for leaks. Very often though, a head gasket leak might not show up until the engine is warmed up. This will help in locating an external leak.

When you see white smoke from the tail pipe, coolant is getting into the combustion chamber and burning along with the air and fuel. The cylinders go through rapid periods of pressure and vacuum. The coolant is drawn in and burned during the periods of vacuum. When there is pressure, combustion gases, (exhaust gas), is forced into the cooling system. Your mechanic has a tool to test for that. It is a glass cylinder with two chambers of dark blue liquid. Air from the radiator is drawn through those chambers. If combustion gases are present the liquid will turn bright yellow.

The third test, for an external leak, is to add a small bottle of dye to the coolant. After driving far enough to warm the engine, you search with a black light. The dye will show up bright yellow. You follow that to the source of the leak.

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