A higher nozzle diameter has the benefit of being able to print faster due to to bigger layer width. There is a tradeoff, you'll have to lower print speed and/or raise temperature to maintain proper layer adhesion. That means that there is an optimal nozzle size for a given print speed/temperature combination. You also don't want temperature too high because it will burn/degrade your filament.
In my experience layer adhesion is quite poor with a nozzle of 0.8mm and it also prevents you from printing finer details (gear teeth for example). The tradeoff versus a 0.4mm nozzle doesn't seem worth it especially if you print overnight.
Almost always 0.4 (sometimes 0.4 stainless). It is the biggest one that still gives me acceptable tolerances, and printing time is easier to deal with than imprecise parts.
Changing the nozzle and recalibrating feels like too much of a hassle for me, so I didn't experiment much though.