Is the wire you have shown, with the paper around the ground (which is NM) the same wire that is coming up out of the ground in the conduit? You posted two pictures in post number 13, one that shows a single cable coming out of the ground in conduit, and another picture that shows two sets of wires connected to a box. Is that where the wire coming up from the ground/conduit terminates? You need to check the cable coming out of the conduit to see if it is UF-B. If it is, then you can, by code, run the things inside the shed using NM-B. UF-B was jacketed in white, and a few other colors, before the universal color of gray was put into place. If the cable coming up from the conduit does not have any colored printing on it, use a flashlight and shine it along the cable from both sides to light up the raised areas where the writing will be embossed on it. This will help to highlight the letters so you can read it. The cable coming up from the conduit may not be the same cable used to wire the light fixture you have shown in post 26. If it does end up to be NM cable in the conduit coming up from the ground, then you have to replace it with either UF-B or thwn wires as others have said.