Yes, you can move verts around afterwords without completley breaking the UV mapping. You can even sub-d the model and still retain proper mapping. Of course, there is always a chance that you will start stretching your texture if you move verts too much, but it is a simple matter to go back to the UV window and adjust a bit to compensate.
As to your second question, The goal of UV unwrapping is to flatten your model out with no overlapping polygons and minimal stretching. LSCM tries to do this, but it will likely need to be tweaked by you manually. Think of a bearskin rug --it was once wrapped onto a 3D creature, but now it’s perfectly flat. -that’s what a good UV map should be like.
it will be easier to understand how UV-mapping works if you load an image into the UV/image editor window (IMAGE>OPEN) and then make a material with that same image and apply it to your model. just make sure the “UV” button is selected under the “Map input” tab in the material buttons (F10) you’ll qiuckly discover how the part of the image that is directly under any given polygon in the UV/Image editor window gets applied to the object. This is why ovelapping poly’s aren’t usually a good thing. (If you wanted to texture a box with the same image on all sides you could stack all the poly’s on each other, but it’s a rare case.)
hope that helps.