]I can't see how they 'can freshen the air.' All they can do is make it move. Obviously if it is situated at an open window, it can 'suck' air into the room or out, depending on which way it is facing.
As for mosquitoes: I understand that mosquitoes 'home in' by flying up stream to the source of carbon dioxide (our breath). On a still night that may be from as far away as 300 yards. Thus if you can disrupt that stream, you can frustrate the mosquitoes, a fan does that.
If a fan is located in an open window, then like an extractor fan (to some extent) it can suck air into the room or blow it out, depending on which way it is facing.
