The rogue vertex may be from that vert not being merged/selected when you unwrapped it. The more opaque section looks like you may have overlapping faces in that area, so maybe you duplicated a lot of faces on top of each other by accident. Try selecting all verts (A) and Merge By Distance to see if that solves the problem.
You can definitely select just that vert and move it. Standard selection and movement controls in the viewport works in the UV editor.
