How many calories are burned by doing 1 push-up?

Insignificant. The point of exercise isn't the number of calories burned, but about toning muscle and getting EVERYTHING to work at a higher level.

If you look at the calories burned for a specific type of exercise, it's a devastatingly small number. But if you look at the number of extra calories that you'll burn by the end of the day following vigorous exercise, it's impressive.