foot got it righ.
sounds like a relay problem or some type of electrical problem. thermostat maybe. i have a 96 accord and i had ur problem last yr and it was 2 main relay. i recommend u to check all relays and whatever u do dont take it to a shop, better off the dealer is a easy fix and cheap. as for the fan stay on after shutdown, it is normal and it is supposed to happen especially n this heat. the fan stay on for a few
btw if ur car is under 150k miles go to the dealer and get a free tune up