1) No. Usually you don't want to use a voltage regulator on a motor. It just burns up a lot of power in the regulator.
Thanks. It takes a long time to get that many points.The Arduino isn't directly powered from the 12V input. There's a regulator to step the power down to 5V. So long as the input is above the regulator's dropout voltage the 5V line will never know there's anything wrong.Of course no existing regulator is perfect. Changes in the 12V input will cause noise on the 5V power. Usually it's never enough to cause a problem.