Sounds like she is trying to figure you out. I think she is testing you to see what she is going to get away with.
Biting-Never hit her in the face that will just cause more problems. You can yell at her and tell her no or give a jab under the chin, not hard just so she relizes its not allowed. I think she is thinking of you as just another horse to horse around with. She is feeling you out.
I recommend round penning if you can. Or work her in a small corral. Also tie her up alot, brush her and pet her everywhere and get to know her . What she likes and what she doesn't like. Carry a crop or a whip if you have to, but never use it unless your are in real danger.
Watch her ears if she is pinning them flat back she means buisness. You need to teach her that its not allowed when your near her. Yell at her clap your hands, chase her, put her to work. Your BOSS MARE not her. When she is doing good tell her she is. She will learn whats good and whats not. Watch some youtube videos on ground work.
Try putting an add out that your looking for someone to give you a hand with ground manners. Someone with a little spare time that isn't looking for money and someone with expierence. You never know, you might get help.