There are no takebacks here, so it is not possible on chess.com.
As for the unrated game, when you create a game, there is a certain slider where you can choose the game to be unrated.
How to set up a friendly game with take backs?


Alright, what about some sort of "analysis mode," where either side can move all the pieces (white and black)? That's really what we need. The classroom setting (under Learn -> Classroom) seems to let only one side (the "coach" side) move.
I realize this is a dumb question, but I can't figure this one out. I want to play a friendly game with my nephew where we can take back moves. How can I do that?
Also, we don't want the games to count towards our rating or anything.
Thanks!