Are there big studies that link diet and lifestyle choices with the probability of reaching a certain age? What are their conclusions?
Many such studies have been conducted to a limited extent in human populations for specific endpoints: for example, using the "Mediterranean diet" will statistically expose you to a lower risk of cardiovascular mortality. Exercising regularly will also have that effect. Basically, every big prevention message modern medicine sends at the population level (don't smoke, don't drink, etc.) is geared towards a longer life, and is supported by literature.
If you want examples, just head over to Pubmed.
However, if you want something more specific about life expectancy, you will have to look at animal research. Well known experiments conducted on D. melanogaster and monkeys raised interesting conclusions:
We can draw an interesting parallel with the present situation in humans, as we tend to reproduce later than in the old days, life expectancy tends to increase, and there are a lot of infertility problems. However, there is no literature to support that those aspects are linked in humans (to my knowledge).