Kim, as far as the biting goes, I can't advise you on how to make her stop, but I am concerned about your safety.
I had a recent incident with our stray. She is very very sweet. I can hold her and rub her belly. I cannot put her in a carrier though.
She scratched me while I was attempting to get her in a carrier to get her shots and spayed. I went to the doctor for a tetnuas shot. He called the Health Dept. To make a very long story short, They wanted to quarentine her for 10 days. They settled for letting me watch her. So, watch the cat for 10 days after she has bitten you or has broken your skin in any way. If the cat hasn't disappeared, you know the cat did not have rabies at the time you were bitten. If the cat disappears within that time, please call your local Health Dept ASAP.
It is rare that a cat would have rabies. Once symptoms show up, it is too late to treat the disease. The incubation period in humans takes longer than it does in cats. That's why the 10 days are important.
Good luck with the biting problem.