I'm not so sure you can lay any of the effects of Islam on birthrates. Birthrates have nothing to do with the basic tenets of the religion, which go towards violence always - note that for a Muslim, there is only two ways of dealing with non-Islam: convert it or kill it. Any peaceful coexistence is seen as temporary, mostly for practical reasons.
And of course Lebanon was destroyed by Arafat and his forces, or at least they set the final destruction in motion. Note that they were Islamic forces. But things had been building up for a long time before that, and the country's Muslim population was already feuding with the rest to some degree, and they were quick to side with the Muslim attackers against their own country, if I'm not much mistaken.
The lodestar here isn't what some one person, or even faction, does. It's contained in Islam itself.