Construction Of Residential House On Land Registered In Deceased Mother's Name

Late mother (Hindu, d. 2013) has three surviving legal heirs - her widower husband (my father), her unmarried elder son (my brother), and myself (unmarried younger son), all Hindu. There's a piece of non-agricultural land (meant for the house) registered in her name. Legal heir document is available in the name of us three. 1. Can we construct a residential house on it? 2. Is transfer of title of the land (mutation) mandatory before initiating construction? 3. Who needs to apply for building plan approval before the civic authority among us three? 4. In whose name Electricity, Water etc. connections need to be applied? 5. House once constructed, in whose name will it be, who'll be its owner? (ghar kiske naam par hoga, ghar ka maalik kaun hoga)