Should an exhaust fan in the kitchen be run with the windows always closed?
Can run.The total result of the the working related to the design of the kitchen.There are two types of design. 1) There will be a hood with exhaust fan and disposable filter, carbon filter assembly in this the fumes and smoke is sucked and filtered and sent out or circulated. Other is an exhausted fixed on the wall and it will suck the air and fumes collected in the room and throws out.In this the suction is from the total air in the room.So opening the windows will help to enter the fresh air into the kitchen.Even if the Windows and door is closed there will be ample space for air ti pass. If the window below is open the total out flow of smoke will be less since it is mixing with the air coming in. Another possibility is some quantity of smoke which is thrown out will come .So according to your need you can run the exhaust with a window closed or open.