Unfortunately, there aren't many cars that would meet all those requirements under Rs 13 lakh. You could increase your budget and get a more premium offering, or be prepared to sacrifice a few things and stick with your budget.
Within your budget, your two best bets are the Nissan Magnite and Renault Kiger, which both offer exceptional value for money. They come with 1.0-litre turbo petrol engines and smooth CVT auto gearboxes, and if driven carefully, can deliver good fuel economy. Their touchscreens are decent but not great, and it's a similar story with their audio systems; neither gets a sunroof.
The Hyundai Exter and Tata Punch facelifts are more affordable but not spacious enough for five, and get clunky AMT auto gearboxes.

