a) Under this "gears" view of star movement how would it be possible for a person on the very edge (south pole) to witness stars near the horizon rotating 360 degrees around him without any particular section appearing closer/larger relative to others? (Can be shown through simple trigonometry to be impossible given star "plains" at a distance of 3100 miles above the earth)
If a person is directly beneath one of the south celestial systems he will witness the stars rotating around him at the rate of one rotation per twenty four hours. The stars directly above him are closer to the observer, the stars near the horizon are farther from the observer.
b)How would stars at the north/south poles with higher inclination from the horizon appear to follow concentric circles which diminish in radius as they near 90 degrees? How would these stars remain in view for the entire summer without ever falling below the horizon?
The stars which remain in view throughout the summer are the inner stars near the center of rotation. If Sigma Octantis (the south pole star) is visible from a location, then the inner stars which rotate around it will also usually be visible. This allows a constellation near Sigma Octantis to stay in view throughout the summer.
The same goes for the stars in the North. If Polaris (the North Star) is in view then the inner stars which rotate around it will also usually stay in view.
c) why would one halfway between a pole and the equator not be able to see where one "gear" ends and the next begins?
This actually does occur:
http://www.danheller.com/images/FAQ/Tech/Stars/img7.html#img10d) If the sets of stars were separate and rotating on opposing axis why do the stars appear motionless in relation to each other from every point on earth?
The stars aren't motionless. The stars are constantly in motion. In the North the stars spin in one direction, in the South the stars spin in an opposite direction. On the equator you will see stars moving in completely opposite directions. See the previous link.
e)Why would an observer on the equator be able to see stars/consolations from both hemispheres at the same time, yet still not observe any opposing rotations?
The stars aren't motionless. The stars are constantly in motion at a rate of one rotation per twenty four hours. Opposing rotations
ARE observed. See the link I provided two questions up. It's a time elapsed star trail taken from the equator, showing opposing rotations.
f) How could two separate observers, one on the very "edge" (south pole) and another 5000 miles to the north both see the same constellation from nearly identical perspectives when it is only 3100 miles away?
The position of the stars in the sky depends on their distance from the observer. It's a matter of perspective, which is why some constellations appear lower in the sky than others.