I think she made these plans before she had discussed it with you, she assumed you would agree to her demands and the fact you haven't has thrown a "spanner in the works" . She is now trying to bully, emotionally blackmail and intimidate you into agreeing.
IMO there is more to this situation, she is way too desperate to get you to agree.
Why exactly does she need to move out? Another poster raised the prospect that maybe she wants to rent to the property out. I don't know but there is something more to this and you are not being told the full story. The full picture would become clearer if she moved in and then I would expect she would be there for many months not just a few weeks.
Also, why can't she pay you any rent, money for bills etc? She made this clear in one of her messages. She didn't ask if that would be okay, she didn't say she would owe you some money and pay when the house was sold, she just told you she wouldn't be paying.
She isn't a friend she is a bully and a CF. A genuine friend would tell you the whole situation, offer to pay now or later but more importantly when you initially said no, it wouldn't work, a genuine friend would understand and accept your decision and then not mention it again.
I understand how you feel, I would haven felt exactly the same if a friend had put me in that position.
This is a situation she has created, she needs to sort it out. This isn't your problem. I think the friendship is over but I don't think it will be a great loss as she isn't a decent or reasonable person and this definitely isn't a friendship, she has shown that she is a CF. Maybe your DP should call her and tell her not to contact you again.