If you are not driving it regularly every 2-3 weeks going out and driving it for 15 minutes would be a good thing but starting it and idling for a few minutes to distribute oil through the engine, transmission wouldn't hurt-the battery won't get a chance to recover though. Longer drives will boil the condensate out of the exhaust as well (caused by shorter run times like start and idle and shutdown).

For some years, car makers have said that no warm-up is necessary: just accelerate and drive slowly from start on a cold morning. I still let mine idle for a minute or two in extreme cold - allowing it to get off fast/start-up idle.

Those who want the car warm when they get in it shouldn't let it idle for long periods, but should install an engine heater: doesn't have to be left on all the time - can be turned on manually or with a timer a couple hours before will be wanted.

Modern cars don't need to be up to running temperature to start out. The recommendation is to idle for 30 seconds then drive. Excessive idling wastes gas and is a wear on the motor.

It could rust, the battery will die. Look a car is made to be driven. It is not a giant toy car or something. Also the tires will deflate faster in the winter. Fluids could freeze depending how cold it is.

For what purpose? You can start it and clear the windows while it is running but all modern cars are designed to be started and driven straight away without causing any damage.

not for very long - long idling will hurt engine