I'm reading a book on doggy body language, so I am going to take a shot at this.
Lying down is a very strong "calming" signal to another dog. Lifting the paw is another signal. The book did not cover the third action you describe
, but my guess is that your boy dog is asking your girl to calm down, and she is showing him she gets it. Kind of an "I'm okay, you're okay."
Also, are you sure it's the hussy part and not the butt part? Butt presentation is also a calming signal.