Choosing the correct power supply for my stepper motor (and other questions)

There's the 5V pin on the power header, and then there are the 20 output pins.

You can use the 5V pin, for maybe 200-300mA total if the onboard 5V regulator is being powered from 12V. The regulator has to dissipate (12V - 5V) x current drawn as heat, and it's just a little chip without much heatsinking.
(12V - 5V) x 0.2A = 1.4W for example.
.5A = 3.5W, the regulator will either go into thermal shutdown, or just plain fail. How many motors did you say?

Don't use output pins - 40mA is absolute max, and a burst of current higher than that can damage the pin and the 328P chip.