Why does my dog tremble when I pet him?
Nudging, wagging, and rolling are three big signs of submission. He's saying, "You're the leader! I know, I know! Please, please pet me to show that you're in control of me!" (Well, something like that. I don't know why he wants petting, exactly, but I know he's being submissive.) Keep petting as normal. This is not a serious problem and should go away in a few months. If you've been feeling stressed out, worried, or scared, that might have done it. He might also have gotten like this as a result of a lot of yelling around your house. Good luck!
Do dogs lick their lips when they're content?
Lip licking is a calming signal dogs use to tell other dogs they're no threat. I would think if she's doing it a lot when you're petting her and she's sleeping, then sighs when you leave...well maybe she thinks something bad is gonna happen(you standing over her could scare her) and is relieved when you walk away.