Yeah that could be a concern depending where you live. Where I live, water is cheap and abundant. And I've never measured, but I would guess I use maybe 10 gallons to wash a car. 2 gallons in the bucket, and just a light wetting followed by soapy sponge and then a rinse, using a nozzle to create a high velocity spray. The water doesn't run at all unless I'm spraying it on the car.

You can probably match that efficiency at home by using an electric pressure washer. Mine does 1.2 GPM, which means an entire car wash is only a few gallons.

That's surprising. I once tried an automated car wash just to see what all the hullabaloo was about and I think the rain actually does a better job. Worst $5 I've ever spent...

Yes. In the same way that dishwashers are an order of magnitude more water-efficient than washing by hand. (But consume a kilowatt of electricity heating the water and running the pump, which is the part that everyone always leaves out.)