First off,never use the crate as punishment.
When my dogs where pups and where at the mouthing stage,I would re-direct them to one of their toys.I would praise them right away.Here I was teaching them that it is ok for them to chew on their toy and not ok to chew on my hand.Or anyone elses.Same thing if they grabbed a sock or a shoe.I always re-directed them to their toy.Ususally a favorite one.Trons was a ball.Yukon's was his football.I always praised them and gave them a treat.Praise is VERY important.They learn by this.And I had 2 to train.Both GSD's and one that joined the K9 force.
You are not rewarding her for biting.You are re-directing her to what she is allowed to chew on.As dee_petlover stated,she bites,you say ouch,she stops,praise her big time and give her a toy.Like I have said,"praise" is they key thing.
I would suggest obedience classes.You say she has a hard time setteling down.These classes will help.How is she around other dogs?
"A dog can express more with his tail in minutes than his owner can express with his tongue in hours."