not normal, i think there was once my eb behave like this, what i did..start the engine again and turn it off. The cooling fan will be running again.

Perhaps you should be looking at Michelin Primacy series. It is built for comfort and quiet.
I won't worry, if the fan turns on and off during normal engine running.

Usually, when the aircon is running, both the radiator fans will spin up... so, when you stop the car, the temp is lower than if you would drive without aircon.

Best way to know, is to have a way to read coolant temperature, such as with the OBD2.

My experience, after I drive slow and steady, the likeliness of fan spin-up after engine off is higher because coolant temp is higher. When I drive faster, ambient airflow is faster to cool down the engine bay...