after i turn the car off the fan keeps running, should it keep running and if so for how long?

 

If the car is to warm it may stay running for a bit to bring the temp down but it should shut itself off.... is the car running abnormally warm? is the coolant up to the proper level?

 

it is rare for fan to keep running in winter time after the car is shut off,, ( well i guess it depends on where you live .). fan should shut off after 10-15 minutes

but as Sir suggested make sure that radiator is full of coolant and no air in the system,, if ok,, could be the switch located at the end of top radiator hose, fan timer, wiring .

 

you have the same problem my 1994 accord has. Has your accord overheaded in the past??? If so, then this is the reason and you have to do something with the fan timer relay or something. i don't know much but that would be the reason and something you need to look in to.