1. Yes, certainly she can lodge FIR against your father alleging rape with or without the promise of marriage,
2. Yes, audio recording is accepted as valid evidence by India Courts,
3. If her complaints are treated as FIR then your father is likely to be arrested for which he should avail AB,
4. On hearing about fer filing FIR, you should file a petition for AB. Develop rapport with local police station so that you can get the information about her filing FIR immediately,
5. You can file any case against her but you shall have to prove your allegation otherwise your filing of case may back fire,
6. It is your father who has to tell her to vacate the house. Moreover, she will be questioned as to how & in what capacity she has entered there,
7. If she can prove that your father had live in ralationship with her with the promise to marry then she can claim her residential right though it will be difficult for her to prove her claim.