Bandage. In wound care, we like bandages because the cover acts as a protectant against further injury and exposure to bacteria that may infect the wound. Specialized bandages also can assist with the healing process by various methods (depending on the status of the wound and the type of bandage. Sometimes a bandage can by irritating or causes an allergic or causes skin tears so the advantage is minimized.
No. Sdrome type of dressing is needed for all wounds you will encounter. Letting it "get air" is old and incorrect treatment slowing healing and risking infection.