Mounting outlet to rubble stone wall
Use a 4-square metal box. Use any common masonry anchors. Anchor into rock not mortar. Half inch ENT (electrical non-metallic tubing) would be a good choice for conduit.  You can use the ENT as a sleeve for the NM cable. Use a 1/2" raised cover and a standard receptacle. You will need a small hammer drill to drill holes in the rock and rock bit. Support the ENT every couple of feet. P.