Adapters, like the one pictured, are available from hardware/home stores to make this type of installation. One of these may be required for light fixtures missing the necessary parts to fit the electrical box. For high ceilings, the threaded rod length can be adjusted to suit most situations.
If the ends of the wires are too far apart, the nut won’t go on properly. Be sure the ends match up before twisting them together. If necessary, snip off a bit at the tip to get them even before attaching the connector.
Use a wood chisel to chip out between the two cuts, deep enough to fit the plate flush with the stud surface. Keep the plates flush with the studs to ensure the baseboard won’t stick out when reinstalled.
A two wire cable run from a light fixture to a switch on a wall. Its only function is to control the on and off state of the light. Underground Feed cable used to run electricity underground. The sheathing on this cable is thicker and more durable than the NM cable used for interior applications.