I'm pretty sure that life expectancy had a huge effect on the world population. In 1950, the world population was under 3 billion. Before 1950 the average life expectancy in the world was never over 50. In 1900, it was only 31! This is thanks to modern medicine and the development of vaccines. That is why our population has grown so quickly over the past century. You also have to keep in mind that infant mortality has gone way down.
Nope. It is due to hygiene. There have been many peoples around the world who have always had general life expectancies in the range of 80 to 90 years - Japan, parts of China, some of the Himalayas.
If you take a look, you will see that medicine and hygiene arrived about the same time in Europe and the Americas. It wasn't the medicine. It was the hygiene practices of the medical people.
