Based on my observations/activities over thirty+ years, I would comment as follows. Others can differ!
The driver will have a torch at night, and may just rely on it and ambient light until they are sitting down, to maintain their night vision. Or could stick on a cab light, perhaps for a while to read paperwork etc. Each to their own! Marker lights will be set for that end for the direction of travel - two whites for forward, red(or reds, could be one or two depending on class/period) if this cab is the rear, one white/one red each end if shunting. The full headlight won't tend to be used where there is good light - stations, yards etc., or when meeting an oncoming train in the opposite direction - you don't want to blind your colleague - so you'll dim the headlight or turn it off. Like all humans, drivers can forget or mess up any or all of these at times!
As you guessed, the marker lights lights each end are set independantly, and stay that way until altered in the relevant cab.
Changing ends requires the engine in idle, brakes applied and no direction set, but the engine isn't shut down.
I am not familiar with the cooling system on the Hunslet, but different classes have different set ups for the fans. I would guess the Hunslets would have a fan controlled by thermostat on the cooling water with perhaps two/three different speeds (aside from off). Cooling tater temperature will vary depending on load, road, ambient temperature, how well the radiators is working (i.e. are the fins clogged with dirt/cement dust like 102's were when it was last shunting at Adelaide).
The engine itself was fine. The cooling system has Marmon couplings in the main pipes from engine to header tank, oil cooler, radiator and such, and if these weren't right, could drip badly. I was told a story (I hope apocrophal) that the Marmons leaked so freely that the water was coming out faster than they could fill the system. The cooling water boiler was to keep temperatures up, the engine warm, everything expanded and avoid frost damage. Ethelene Glycol tends to be added to the cooling water, certainly these days, but was not always used. Antifreeze will not, however, help a cold battery crank an engine - starting stuff in the cold can often be a pain.