Do unrated games affect your time/move? I know /*think* they don't affect your total games played or average opponent rating, but I'm not sure about time/move...

unrated games are only played for the sole purpose of having fun. It does not affect your rating and do not affect your total games played. As for time per move, I think it does but dont think its important to know that.

Not me. I still get very similar win/loss ratios whether the game is unrated or rated. (same distribution of opponents)

The only type of unrated games which will affect your time per move is greeter games.