Yes, they can stay plugged in when not in use. However even if the car is not running, the charger will continue to use a small amount of battery power, even if there is no device plugged in. This could affect the battery of your car if it is not driven for long periods of time.
This is not abnormal. Please try using a different charging cord or a different outlet to test if the product makes this sound no matter what the conditions are. If you are still dissatisfied, please contact our customer support team.