I think you need to do a bit more research on the shape of the universe and the position of the earth in it. Here is one place to start that might address your second point of confusion - the movement of the sun in relation to the galaxy in which it is located -
http://en.wikipedia.org/wiki/Milky_way - and you should follow the included links to examine the movement of the Milky Way in relation to its super-galactic neighbors and the cosmos in general.
The universe does not revolve around the earth, or the sun, or the Milky Way, or the Local Group, or the Virgo Supercluster, or really anything else. Everything moves in relation to other objects, and you have a lot of reading in front of you to begin tracking them.
As for what the "universe" (I presume you actually mean the night sky?) would look like from some point on the opposite side of the universe from earth, yes, it is possible to calculate that. The relative motions of stars are very slow on a human time scale, and at least the stars visible from earth have been fairly thoroughly mapped in three dimensions. From that mapping, a star chart centered at any point in the universe can be calculated using some basic spherical geometry and optical physics. You can do this yourself - pick a point in the universe, start looking up star coordinates, sizes, and light outputs, and calculate where they would appear in the night sky of your selected point and how bright they would be.