It is very hard to know much because the news reports are mainly conjecture, rumor, and opinion. Facts are few. The one important fact that I think ended the war was the impending American delivery of M-26 cluster bomb barrage rockets and bunker-buster bombs to Israel (New York Times a few days ago). Had Israel had those at the beginning of the war, each Hezbollah Katyusha rocket crew would have died within minutes of launching their rockets and their launchers and rockets would have been destroyed as well. But Lebanese civilian casualties would have been in the thousands or even tens of thousands, which I suppose is why the US delayed delivering them.
I think the timing of events confirms that theory. Nasrallah was defiant and willing to fight forever. Then the impending transfer of M-26's and bunker-buster's was announced and Hezbollah immediately agreed to a ceasefire. I have not seen a followup to the story about the M-26's so one does not know whether they have actually been delivered or are being delivered or what. I think it is like one of those movie scenes where the heavy pulls back his jacket just enough for you see the pistol. The threat was enough.
The significance of the ceasefire cannot be known without knowing what the actual outcome of the battle was. There are no credible reports of the casualties and damages suffered by Hezbollah. The reports were always the same, "fierce fighting" but no indication of the outcome. The only indication of the degree of damage is that they were able to maintain a rocket barrage against northern Israel in spite of the bombing and artillery bombardment, and that Israel felt obliged to send in the infantry. Both facts suggest that the damage to Hezbollah was not fatal.
As to how the world is going to deal with Islamofascism in the future, I think we just saw. We are going to have to kill enough of them to get deterrence. We are going to have to choose between inflicting large civilian casualties and defeat. The war with Iran will be like the war with the Soviet Union - fought through proxies.