At any given time our rotation is not affected by our motion around the Sun; we just keep rotating the way we "always" have, so during a given year the direction that our polar axis points in the sky stays nearly constant.
However, over long periods of time the fact that we do not rotate perpendicular to our orbit, but at an angle of roughly 23 1/2 degrees to the perpendicular, combined with the oblate shape of the Earth (due to its rotation, it is 1/3% wider at the Equator than through the Poles), causes a torque or twisting effect on the direction of the rotation (primarily due to the gravitational effects of the Sun and Moon, but to a lesser extent, even Jupiter). This is exactly like the way that a top rotates around a perpendicular axis when it is tilted away from the vertical (it is also why tops are wider sideways than vertically). On average, the angle of 23 1/2 degrees stays the same (there is a small 18-year variation, called nutation, caused by the tilt of the Moon's orbit relative to ours, and the fact that the Moon's orbit rotates around a circle once every 18 years, but it is insignificant in comparison to the 23 1/2 degree average tilt), but the direction of the tilt moves around a circle centered on the point in the sky perpendicular to our orbit (the Ecliptic Pole) once every 26,000 years. As a result, which star is the "North Star" has changed dramatically over the ages. In Egyptian times, Thuban was the Pole Star, in Hellenic times, Kochab was the closest star to the Pole (though not nearly as close as Thuban had been or Polaris would be), and at the moment Polaris is the Pole Star. But over the 26,000 year period, stars scattered around the 47 degree wide circle centered on the Ecliptic Pole succeed each other as the Pole Star, and there are long periods of time when there is no star particularly close to the Pole.
For a diagram showing the motion of the Pole over the last few thousand years, see the page about Ursa Minor, at http://cseligman.com/text/atlas/ursaminor.htm
The first diagram on the page is an old map of the constellation, which includes part of the circle that the Pole follows around the sky over its 26,000 cycle of precession. The second diagram shows where the Pole was on various dates. You can see that it has only been close to Polaris for the last few hundred years, is now about as close as it will ever be, and in the future, Polaris will gradually be left behind the precession, so though it will be the North Star for quite a while longer (our lifetimes and then some), it will gradually become a worse and worse indicator of where true North is.
It doesn't really. There is no energetic interaction of any noticeable effect between Polaris and Earth. It has not always been the pole star and will cease to be after some centuries
Due to the wobbling of the Earth’s axis, the north star always changes through time. Polaris is the north star now, Vega was the north star about 12,000 BC and it will be the north star again in about 13,000 years from now, in about 8,000 years Deneb will be the north star. Consequently, because the wobbling of the earth’s axis, the north star changes through time.
It does not, as Earth's axis can be displaced by 9+ earthquakes like Fukushima's.
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