My Dog put's her paw on my new puppy's back?

She is letting him know that she is the dominant dog in the household. Just monitor her and make sure she doesn't get too rough! She's still figuring him out and letting him know who's boss. If you see her play bow at him, then you'll know that she "likes" him and is inviting him to play. Following him around sniffing him just means she's trying to figure him out. Congrats on your new addition!