1. She has no legal right to stay in that house against your asking her to vacate it. You had only allowed her to stay therein i.e. gave license to her to stay in your house which you want to be vacated by her now.You shall have to file an eviction suit against her being the licensee,
2. If she had managed to make a lease deed with you, then she shall have to vacate the leased premises after the lease period is over, if the said lease has not been renewed by you. File an eviction suit for vacating your premises by the leasee,
3.Yes, as sugggested earlier,
4. After the property has been gifted to you by your father by executing and registering the Gift Deed, then it is now your property whereupon you have the absolute right, title and interest legally. She wont be able to claim any share from it legally.