|MadSci Network: Astronomy|
I like this question. It has a lot of possibilities for inquiry into how the solar system and the earth work. To answer the first part about why the earth is tilted, I have included a link to a very similar answer to help. Someone else asked a similar question before. http://www.madsci.org/posts/archives/nov99/943922199.Es.r.html To be perfectly honest, we really don't know why the earth is tilted but we have some ideas.
The solar system started out as a large cloud of gas and dust called a nebula. This cloud was not uniform so when it started to collapse because of gravity, it didn't collapse evenly and it started to rotate. As it collapsed more and more the rotation increased, much like a figure skater increases her spin by drawing in her arms. The central portion eventually formed the sun. Around the sun, other parts of the cloud began to condense and form small bodies called planetesimals. These were about the same size as the larger asteroids are today. As these planetesimals moved around the sun, they gathered more and more material until the reached the size they are today. They were already moving around the sun in orbits and probably had some spin from the collapse of the original nebula. Because of the spin and the motion around the sun, these planetesimals didn't grow uniformly. This is probably where the tilt of the planets comes from and the reason that the tilt for each planet is different. Uranus, for example is tilted almost 98 degrees.
When the earth was forming, we know that objects of various sizes struck it early in its history. In fact, the current best theory of the formation of the moon is that a planetesimal the size of mars struck the earth and the ejected material formed the moon. What was not ejected merged to form the current earth.
Because of the gravity of the sun, moon and other planets, the earth's motion around the sun is a very complicated motion. You asked about Polaris. Polaris just happens to be the North Star now. The poles of the earth wobble slightly with respect to the plane of the solar system. This is called precession. It takes the earth about 26000 years to go around once. During this time, the North Pole will move away from Polaris toward Vega and then back to Polaris in a very large circle over the next 26000 years. Try this web site for a better explanation. http://www.physics.wsu.edu/Courses/astro/html/lec-precession.html Another consequence of this is that the earth's tilt also wobbles a bit through time. It is now about 23.5 degrees and this about the average. It does vary from about 22 degrees to a maximum of about 24.2 degrees.
Try the links in the MadSci Library for more information on Astronomy.