My answers are as follows:
1. Can my father sell the land without the permission of his children?
Ans: Yes, it is his absolute property inherited from his father and not ancestral property ( because it is no history of four last generations)
2. Is it possible to file a caveat in court so no objection can be filed by my non-cooperative sister for selling the land ?
Ans: Not necessary.
3.Is it possible for my father to unilaterally gift this property to all his children under the condition that they should sell the property and equally distribute the proceeds among themselves?
Ans: Yes, he has that right. But your unwilling sister may bring a stay and prolong the matter.
4.Can my father make a partition deed and equally distribute this property without the consent of his children?
Ans: During the life of your father he is the absolute owner.