When I tell my puppy off he sometimes rolls on his back as if he wants a tickle or is pretending to be tickled? Does he think I am playing or is he just trying to look cute? What is he doing?

He is showing that he is submissive to you. He wants to show that he is no threat to you.

I agree with Emland, your dog is in a submissive position, showing that you are in charge. It's a great thing, showing that you are alpha in the house, just make sure his submissiveness doesn't turn into fear.

He does not understand what the command is. When you told him "off" he got confused, so he just rolled over to try and impress you.

I agree with both of you submission is a great sign.