(1) My father had some self aquired property and had relinquished his rights over his ancestral property in favour of his 2 younger brothers, though not in writing.
COMMENT: If your uncles have occupied shares in the ancestral property excluding your father since the alleged oral relinquishment by your father, and if minimum 20 years have been passed, then by the effect of Law of Easement your uncles will be considered owners of their respective shares and the alleged relinquishment by your father will be deemed to have taken place. But if your uncles have never occupied any share in ancestral property and the ancestral property is unpartitioned, then the unwritten relinquishment in favour of your uncles, has no meaning. All heirs of your father including you, can still demand your father's share for partition among yourselves.
(2) There was some self aquired property in the name of my mother also. My father died in the year 2003 and my mother also passed away in 2007 without leaving behind any will.
COMMENT: As both your father and mother died intestate, all heirs should get equal shares of self-acquired properties of your parents.
(3) We are 2 brothers and 3 daughters and I am the youngest son. I have filled a partition civil suit under the Hindu Law of partition demanding my share in the self acquired properties of my parents.
COMMENT: All heirs can rightfully seek partition of self-acquired properties of your parents on their dying intestate, you are also among heirs of your parents.
(4) I am not interested in any share from the ancestral property of my father as my father's share would be very little to be of any value after repartition among his wards.
COMMENT: Mentioning that, you are not interested in the ancestral property is not necessary for the partition suit.
(5) My 3 elder sisters are supporting me fully as my elder brother is not in good terms with them. My elder brother is not agreeing to the partition and has now filed an affidavit in the court denying my father's relinquishment of his rights over the ancestral property. He is demanding that ALL property of my parents (self acquired as well as ancestral) should be placed in the hotchpot before partitioning.
COMMENT: There is NO LAW making it mandatory that all properties (self-acquired+ancestral) of a Hindu Male/Female dying intestate, should first be joined then partitioned. Therefore even if your elder brother succeeds in establishing that your father had never relinquished his rights in the ancestral property, still your father's self-acquired property can be partitioned separately among his heirs. If one of heirs dissent to partition, property can still be partitioned. Your father's share in ancestral property can be alienated later for partition. So, your elder brother's demand for joining all your father's properties first, has no value. Your father never got his share in the ancestral property, so that share cannot be included in his current properties.
(6) The problem is that the said ancestral property has not been mutated since 4 generations and my elder brother is using that to linger the matter and cause delay in partition.
COMMENT: The ancestral property should have been mutated at earliest possible opportunity, but in partition of self-acquired property of your father it is not an obstacle. As the ancestral property can be separately partitioned, it can be mutated just before it's partition.
(7) (i) Is there any law/bylaw etc. which I can use to separate the ancestral property from the self acquired property and demand that the self acquired properties of my parents should be partitioned separate from the ancestral property of my father?
COMMENT: Self-acquired properties of a Hindu Male/Female dying intestate, can be partitioned independently of his/her share in any ancestral properties. Therefore, you don't have to specifically demand for it.
(7)(ii) Till now, my sisters have not replied to the summons served to them and are set exparte. Should they file their replies or remain exparte?
COMMENT: You can succeed in your partition suit and if your elder brother contended his demand in this partition suit then I don't think his demand will be taken into account by the court but you can argue against his demand according to what I explained. If your sisters have been served summons in the same suit, they should file their replies. A separate suit for demanding that first all properties should be joined (should be placed in the hotchpot), is not maintainable.