1. If your grandmother is not making any Will bequeathing the proeprty to your name, then the property shall devolve equally on her legal heirs.
Since your father was the only child to your grandmother and he is also no more living, then the property left behind by your grandmother upon her intestate death shall devolve on the legal heirs of her deceased legal heir, i.e., you.
You can get a legal heirship certificate of your deceased father and your grandmother also after which you can submit an application to transfer the revenue records to your name, subsequent to which you will become an absolute owner of the proeprty left behind by your grandmother.
2. Yes the registered gift deed on the name of your grandmother shall be the title document to declare her title to the property.
3. You would require the original registered gift deed standing in the name of your grandmother, the document by which the donor gifted this property to your grandmother, tax paid receipts, patta, the death certificate of your father, legal heirship certificate in respect of your father and that of your grandmother too.