Quote - When I move the points on the UV map am I messing up the mesh points?  IE do the points on the model move at the same time?

As a general rule, no.  The UV mapping has its own set of coordinates.

Quote - Does it matter if these dots are in a jumbled mess as long as they don't overlap eachother?
Does overlapping even matter?

How jumbled and overlapping are we talking here?  Try to look at it from a texture-painter's point-of-view.

Overlapping parts that will be divided among separate maps (body textures vs. head textures, for instance) are okay.  Overlapping parts on the same map, however, might cause texturing problems.

The ultimate goal of UV-mapping is to flatten a three-dimensional object with as little distortion as possible.  And for continuous surfaces like organic bodies, with as few seams as possible.  Good UV-mapping is as much an art as it is a science.