Construction of residential house on land in late mother's name.

Late mother (Hindu, d. 2013) has three surviving legal heirs - her widower husband, her unmarried elder son, and self (her unmarried younger son), all Hindu. There's a piece of non-agricultural land registered in her name. Legal heir document is available. 1. Can we construct a residential house on it? 2. Is transfer of title of property (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)