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.
USB- PD enables compatible devices to charge at higher voltages and supports bi-directional charging and data transfer from both host and peripheral. Charge your USB-C phone at 5V 3A and your MacBook with the same cable and PD compatible charger. Get more detailed information from our Power Delivery blog post. (https://www.aukey.com/usb_power_delivery)
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.