Proportion of sale of Property among Chidren

Hello, I have the following query. Would require your valuable inputs to have more clarity. My father was in Karnataka state Govt. service. He acquired a house through his earnings from Karnataka Housing Board. After his death in 1979, the house property records were transferred to my mother’s name. My father did not execute any will. My mother is a family pensioner and pays the property tax as on date from her income. We are 5 Children, 1 Daughter and 4 sons who are all majors and settled separately. My mother who is 82, wants to divide the house property under these circumstances, please clarify the following. 1. Is my mother legally empowered to execute the will at her discretion or give the power of Attorney to anyone? 2. In case the property is sold in what proportion the sale proceeds are to be distributed between my mother and 5 children? 3. In case of a sale, is it legally necessary for my mother to have authorization from all her children? 4. In case, one or more children are not happy with the proportion could they create a problem later on? Your inputs are eagerly awaited.