Are lunar occultations visible to the naked eye? The Moon occults a lot of stars. But are these events visible to the naked eye? Won't it be blinded out by the crescent even at its thinnest just before sunrise? Did ancient astronomers actually observe them, or did they deduce them theoretically according to orbital calculations? (I suppose occultation during an eclipse is both invisible and unlikely, right?)

Venus, the brightest planet, like the new Moon always stays near the horizon. But could one actually see even Venus disappear behind the lunar anti-crust? A popular medieval islamic symbol suggests to me that they were well aware of this phenomena. Both the Moon and Venus are still symbolically important in their culture. But was occultation directly visible or inferred?
Yes - especially as the occultation does not have to occur on the bright side. Planets may also be occulted (see http://www.lunar-occultations.com/iota/planets/planets.htm)

Incidentally the symbol is not originally Islamic. It was the flag of Constantinople when conquered by the Ottomans and then adopted by them. The Ottomans later became the Caliphs - the nominal leaders of the world's Sunni Muslims and so the flag was widely adopted across Islam.