The K series head gasket can fail either by way of the elastomer beading degrading (due to excessive heat) or by failure around the fire rings (which is quite common). In the case of the latter, exhaust gases will be forced into the coolant system, so yes, a sniff test will verify if there is failure of one or more of the fire rings. A sniff test will only act as confirmation a failure by revealing excessive levels of hydrocarbons in the coolant; it won't confirm that the gasket is sound because there are always some traces of hydrocarbons in the coolant, and these will be detected. It won't tell you if the elastomer bead has failed - If the head gasket has failed and you are loosing the quantity of coolant you state (and you say there are no signs of external leakage), there will be signs of condensation or emulsified oil on the dipstick or within the oil filler cap.
There are several explanations for coolant loss - simple leaks in the system pipework, radiator or heater matrix; failed seal or pressure valve in the expansion tank cap; leaking water pump; or inlet manifold gasket failure, as well as head gasket failure.
If the IMG has failed, there is often a misfire for a short time after first start up.
I would say your squealing belt is very likely to be the alternator belt insufficiently tightened.