Yes, because your engine is on.
If it runs even with the car shut off it is probably a bad switch. If it runs all the time with the engine running it is probably a bad temp sensor.
Volkswagen has a hardwired cooling system in a good number of their models, the cooling fan will run several minutes after driving. Especially if the engine is overheated, you can expect the fan to resume after it has initially shut off... So make sure to disconnect the battery before any repairs following running the engine. Brandon 1990 volkswagen jetta gl 1.86 carrat Wolfsburg edition
I would check the Cooling Fan Switch/Relay. Sounds like it is a bad switch and stays 'on' well after it is needed, if it is running the battery down.
When it's running hot you should hear the cooling fan running, if not that is your problem. If the cooling fan does not operate check the fuses, cooling fan relay, cooling fan switch and cooling fan motor. One of them is at fault.
Most likely yes , the engine thermostat has failed in the open position - happened on my 1995 Ford Explorer even though I have always had the cooling system serviced
As long as the engine is running, this is normal.
If it runs all of the time, even if the engine is first started inthe morning,Then the temp sensor that controls the fan may be gone.
The fuel pump runs constantly as long as the engine is running.
I can't speak for that SPECIFIC car and model but on most cars with two fans, one is driven by the engine belt and runs whenever the engine is running. The other runs electrically and can turn on (usually) if the key is in the ignition. There is a relay and a controller that tells that fun if the engine needs cooling. On some cars this fan will run even if the key is not in the ignition; i.e. parked and the driver away from the vehicle. It should stop when the sensor running it decides the engine is cool enough. Both fans are electrically driven and have two speeds. The fans operate at a lower speed until a certain temperature is reached, at which time they both switch to high speed. The two fans are always on the same setting: Off, Low or High.
Maybe your cooling system needs to be flushed out.
Fuel pump
If the vehicle has an electric fuel pump, then no, it runs no matter if the engine is running or not, but it will only run for a few seconds unless the engine is started. However if the pump is mechanical then the engine must be running for the pump to work.