After your father's death, his estate devolved on all his Class-I legal heirs automatically in equal measure. In other words, your mother, your sister and you got one-third undivided share each. If your father's mother was alive at that time, she too was entitled to a share, in which case the four of you inherited 25% undivided share. Assuming that it is your father's estate, this is the distribution. Your mother can leave a Will only in respect of her undivided share.
If it is the question of your mother's self-acquired property here, your mother can write a Will in favour of anyone of her choice.
1. In a Will, there is no question of any male or female beneficiary. It is your mother's choice.
2. No. A share in an immovable estate is quite different from her marriage gifts.
3. She is very much entitled to her share if it is your father's estate as explained above.
4. No, legally there cannot be any such claim.
5. Yes, you may engage a competent lawyer.
6. Go by your lawyer's advice.