Does Edward hug or kiss renesmee?

yes. in "breaking dawn," the volturi walk away for a moment to discuss whether or not to kill the Cullens and the wolves, Bella gives Renesmee to Jacob and tells him to run away with her and take good care of her. right before he leaves with her, edward hugs her tightly, then kisses her forehead and both her cheeks, and tells her he loves her and that she better be good.