Given two vertices that are “linked” together by an edge, how do I remove the connection between them? Basicly I have a vertex, I extruded it, but I have an edge between the two, and now I want to remove it. If I press x and remove the edge … it removes the terminating vertex to. Can I go around this?
Go ahead and delete that vert and a good way to get a new unconnected vert is to make sure that you have nothing selected and Ctrl-LMB where you want the new vert.
Oh boy, was affraid of that, I’ve got 22 verts that need to be in a certain position. Hmm … I could duplicate them 
Try X > Edges & Faces.
I duplicated them and it worked 
Control LMB adds a vertex. Deselect All before each one, and they won’t be attached to anything.