FM transmitters allow you to play music or other audio from your phone with your car speakers by using a FM station. The station must be one that is not used in your area to avoid a static connection.
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.
It is normal for a little heat to be emitted from the product, but it shouldn't be too hot to handle. In this case, please stop using the product and contact our support channel for more help.