yes, there is a nozzle to let any excess water escape, to avoid over-pressure.
no, you should not lose coolant, unless you put more than the maximum (refer to the above).
It takes more than the MIN to light up. I had a punctured radiator and was losing coolant once, but despite the whole secondary tank (the plastic one) was almost totally empty, yet, i wouldn't have a warning light. so it seems that you should lose water from the radiator to have the light.
BTW, i think it's time for you to go check your cooling system... nothing to be afraid of
