I found the following answers.
(1) Reason for odd departure times for flights to the US from India was bothering me for few years. I caught hold of a flight attendant on my return trip to Austin, and asked him this question. He said that they do this primarily for three reasons: (a) day time temperatures in India are usually very high. Take-off during hot weather wouldn't be as smooth as in moderate weather, esp. for jumbo jets (b) planes consume more fuel for take-off during hot weather and (c) leaving India close to midnight would enable passengers to reach the US at a reasonable hour (i.e., during business hours). Makes sense to me, but did not verify this information against a published source.
(2) Using Google, I found that Great Circle distance is the answer to my second question. I used Great Circle Mapper to plot the flight path for a better understanding. I am still a little confused as the mapper shows that the shortest distance between Newark and Mumbai as 7,800 miles, while our flight traveled ~ 8,300 miles (about 6.5% more than the Great Circle distance). Perhaps this is due to slight deviations from the course (to avoid turbulence, navigational equipment limitations etc.).
Finally, while we were flying at ~ 37,000 feet over Greenland Sea, outside temperature was -90 degrees Fahrenheit (~-68 degrees Centigrade). Sitting in a metal tube 11 kilometers above ground, with temperature = -90F a few feet away, 50,000 gallons of fuel on fire 15 feet below, watching TV and eating hot food, totally oblivious of the deadly surroundings? What would Wright brothers think if they were brought back to life today?! Our technological progress is amazing.
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