India is vast and there are varying weather patterns - summers tend to get very hot, and is best avoided. Whereas from October to March you'll experience the warmth of winter, as the Himalayas stop the cold winds. This is a much more bearable time to visit, as July to September is monsoon season.
India is the second largest country when it comes to population size - in 2016 there were 1.324 billion people in India. You'll definitely notice the marked difference between the US and India in terms of population as soon as you arrive! Mumbai has the largest population in India, followed by Kolkata, Delhi and then Chennai.