The Islamic symbol is of the crescent moon and a star (Venus) extremely close to the moon. How often does this occure and how did it become such an important religious sign?

The star and crescent symbol actually predates Islam and was later, after a complicated history, adopted by the Ottoman Empire. It is not certain that the star is supposed to symbolize Venus:

https://en.wikipedia.org/wiki/Star_and_crescent

Exactly how often Venus and the crescent Moon are in close communion I'm not sure -- there must be some astronomers on the site who could answer this -- but here's a rather charming press release issued on the subject in 2004:

http://skytonight.com/about/pressreleases/3308711.html?showAll=y&c=y