@Tami1
Yep...had this happen also. We were able to get the stains out of the pillowcases using hydrogen peroxide and letting them soak in it. Not sure about counter tops or walls. You can try using a magic eraser, but not sure that will work?
I would reimburse for the nights not stayed. I would deduct the cost of addl cleaning for the hair dye damage from one of the days they are asking 30% refund. Guests threaten to sue all the time and most times it's idle threats. I wouldn't worry about that. Be sure to keep all your evidence of the damage from the hair dye. Airbnb may override your deducting damages from one of the days they are asking to refund. In that case, I would file an Aircover claim and expect the guest won't pay. Then Airbnb will have to cover, but you will have to jump through the usual hoops.
This guest will most likely leave a very negative review, so be sure to leave an honest, factual review of her and the damages from the hair dye. Take responsibility for the heating issue and what you did to resolve it.