Is there anyway to remove a line between two vertexes like to unjoin them and them alone without disturbing all the other vertexes connected in other ways? All I know how to do is delete them, and that at times causes me a world of hurt.
X -> dissolve edges. You can join them again by selecting vertices and press J.
note you can always press ctrl z while in edit mode.
And if it all went terrible wrong in edit mode, go back to object mode, press ctrl z to undo all last edits.
advice learn a bit about undo and redo, and the different effect of mode when you do this.