All of your answers are going to depend upon the specific dept & their rules/procedures/union contracts. - Is the firefighter allowed do simple maintenance like change the blade/chain on a saw or does a qualified mechanic have to do that? For things like an oil change does the fleet mechanic come to the station; does he come to the station with a reserve piece of apparatus so the engine doesn’t need to go out of service during said maintenance, or does the crew drive to the fleet garage for that to be done? If the latter, does only the driver go or does the whole crew go for the ride so they can respond to calls within the first/last 2/3/5 miles from their station?
I answered the off-duty call in piece over in that thread.
For things like training/recertificaiton, that’s usually scheduled at other times so that the firefighters can go to the academy & sit & take the class w/o being toned out for a call but just because I said that, I’m sure there’s some dept that has a trainer go to each station, multiple times to get all of the crews & trains them there & if they get a call, he just sits there until they come back.
Probably give the truck a once-over at the beginning of a shift to make sure everything is where it’s supposed to be & at some interval - daily, once or twice a week, again varying by dept start all of the tools up & make sure the gas tank is full or battery is fully charged; it’s not unheard of for something to look like it’s there but not be sitting properly in the trickle charger so it’s not really charging.
& yes, if you get a quiet night, you get paid to sleep. OTOH, you may be a hurtin’ pup some mornings.