is proxima centauri always 4.4 light years away from the sun? does it get any further or nearer than that? and how about it's position in relation to the sun(east/west/inclination)?

If you look a star up in Wikipedia it will usually give the star's proper motion and radial velocity. The radial velocity is what you are asking.

http://en.wikipedia.org/wiki/Proxima_Centauri

http://en.wikipedia.org/wiki/Radial_velocity
http://en.wikipedia.org/wiki/Proper_motion

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What brings us together is stronger than what pulls us apart

It must be pointed out that there is still much we are unsure of here. This 'Proxima Centauri' may not be gravatationly bound to the Alpha Centauri double. It is near to them., and most likely is part of the group. Movement is the normal not the exception.
'Argos' has supplied the best yet future model. Wikipedia, thanks.

Its distance will not change noticeably any time soon.

As the earth orbits sun, since proxima is near to the sun, it would change its coordinates on the celestial sphere, its RA and declination; in a repetitive 12 month parallax cycle. but since it's about 1 parsec distant, It would only change coordinates by 1 second of arc in that cycle.

our solar system is orbiting the galactic center, as is proxima centauri. As mentioned above, it has a velocity different from that of our solar system so it will change its position relative to our Sun over time. It will appear to change position relative to more distant stars as well.

In 100,000 years a great deal of the sky will have been recycled, as present stars with great proper motions recede from view and new ones come into the scene.

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What brings us together is stronger than what pulls us apart

The title of the thread is actually kind of interesting, because you ask the question "does it ever change"? It almost makes it seem like it might suddenly start moving. In fact, it is changing constantly, so proxima centauri is not the same distance from the earth as it was when I started typing this sentence. Not that it makes a big difference.

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As above, so below

When I sit out and watch the stars I have to remind myself that they are all moving--but the sky I look at is virtually identical to that of several thousand years ago.

Is it only because of the proper motion of the stars themselves, though? Or does our movement around the galactic center also play a role?

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"Science is physics and astronomy." -Me
"There is absolutely no law in physics that prevents time travel." -Dr. Michio Kaku

The orbital motion around the galactic center is the basic cause of all of this. The observed proper motion of a star as seen by us is a result of differences in the orbital motions of the Sun and the observed star.

Looking at the bigger picture and, we can never do this. We must use imagination to conceptualise the image... that we can do. Looking down ( or up ) at this Galaxy from a distant point of view at right angles to its plain. It would look like a large decathlon wheel with spiral arms and a central bar. Artists impressions are available.. check Wiki...? its there. Its rotating about its central mass and core. Local gravity influences the movement locally. We can not see a great deal of movement because we do not live long enough.