Hello,
I was wondering, is there a reason to have the fan always on, even while not printing?
Quick answer is no. On all Tiertime printers, the fan stays on unless you select the dormacy checkbox on the print screen, however you cant do this with the Cetus as the arm would drop onto the print as it effectively does the same as a power cutoff. There is no way of controlling the fan independantly like in other slicers (may be able to do it with the GCode upload feature but havent tested this).
YES, because it also help cool doen the throat of the nozzle where the filament goes in. Since the nozzle piece does not have a heat sink like other designes, it can get hot and your filament will jam.
I'm pretty certain that the cetus fan is just wired directly to power and not output controlled by the board. It can be a little annoying if the printer isn't being used but, at least in my case, i just turn of the printer if I'm not using it.
I turn it off too, but that's not ideal :)