Moving and covering light fixtures in bathroom
How you get the wire there depends on framing, access, etc. Hard for us to say. Ideally you have a continuous cable from the switch or power source. Old wires need to be disconnected at both ends.
Ditto. 
You can't cover junction boxes that are in use. You'll need to have a continuous cable from your switch, or you'll need to put a decorative plate over any remaining boxes and keep them accessible.