Moving to Lucknow!!

Hi, We are 33M/34F with 2 kids, who are almost 4 Years old. We plan to move to lucknow. Currently, we are in the USA. We aren’t from Lucknow but a nearby city. We plan to buy a house (No Flat) in Lucknow preferably in a gated society. Our budget is 2-3Cr. I need your help with the below questions: 1. Recommendations for good gated society, which has houses/Villas in 2-3Cr. 2. What are the good schools, not looking for IB schools. Atleast when i was in Lucknow, La Mart and St. Francis were considered good. 3. For a Family of 6[ Couple, 2 school going Kids , Parents], what should be the yearly budget/expenses. 4. I don’t plan to work but may be a side gig, any recommendations?