Dear Sir,
My answers are as follows:
1.Can I get the property by asking my mother and sister to execute relinquishment deeds giving up their shares(one-third each) in the property to me ?
Ans: Yes, it may by a) relinquishment deeds b) release deed or b) a merely NOC, if you can manage the authorities. Family heir ship you have to produce.
2.If I buy-out their share in the property from them will they be liable for capital gains tax though it is not a sale ?
Ans: Yes, they are liable.
3.As no mutation has been done since my father's death till date will that have to be done first (entry of my mother's name, my name and sister's name) and subsequently the 2 relinquishment deeds submitted or can the mutation be done straight away in my name by submitting the relinquishment deeds ?
Ans: It is better to transfer directly in your name by producing the relinquishment deeds of your mother and sister.