Transfer of property to the legal heirs

Since your father died intestate and there is no will, the partition will be done according to Hindu Succession Act. You, your mother and grandmother, all three are eligible to 1/3^rd share of the fathers property.

Yes, your grandmother also has share in the property.

For transfer of property in your mother’s name, a relinquishment deed has to be prepared and signed by you and your grandmother. It should be duly stamped and registered.