Mine sheds in pieces..Larger pieces for the back and smaller "shreds" for the legs and fet. I've never had issues with his hands/toes not shedding well. I think if you provide a substrate like topsoil and rough items in the cage, the skink can easily get the shed to come off with enough humidity. I've never seen mine eat his shed (like my geckos do).
My guy will eat crickets or roaches... I even froze roaches from my dubia colony when it got too large and he would eat the frozen-thawed roaches. I could not get him to touch hornworms though.