The move Edge(s) is not Nurbs modeling so you must change a little your Poly modeling habits :)

Yes you can but...it's pure poly modeling so no need! :)
As you see I don't move the segment but it's Vertices!




and for adjust you can use the Scale ;)



and for adjust an object on another one you have dedicated tool Orient "Line Line" ;)
with some options : Uniform, Stretch, None...here stretch



etc...