I am looking for a database about death rates and population around the world.
Idealy, I want:
- Per country
- Per year
- Including birth rates
- Divided by gender
- Including age of death
The World Health Organization Mortality Database is probably what you're looking for.
The CIA's World Factbook contains everything you ask except it has data for only one year.
The United Nations Statistical Division publishes an annual yearbook of statistics (including birth/death rates) by country. The latest addition is 2012
There is no more reliable database than Human Mortality Database -- mortality.org. This database is run by demographers who use state-of-the-art methodology to overcome issues in the data. As the result, the estimates are as precise as possible. Their methods protocol is a masterpiece of demographic data processing. On the down side, the data of decent enough quality is available for only a bunch of countries.
To explore the data I highly recommend Human Mortality Database Explorer.