Close, but not quite. The North Star is actually at declination 89 degrees, 18 minutes, so it is 42 minutes (not quite 3/4 of a degree) away from the exact celestial north pole.
The North star is called Polaris. Polaris is the brightest star in the constellation Ursa Minor. It is not the brightest star in the night sky; that title goes to Sirius, in Canis Major. Polaris has...
Surprisingly, no. This is the star the wise men saw when they were walking to find baby Jesus in the manger. Then, it was north. However, it is not always in the north.