You are indeed good, Forscher, except for one or two points.
"After that, Islam was spread through conquest"
That is incorrect. The Islamic Empire, in the sense of a political entity governed by an Islamic warrior elite, was certainly spread through conquest as the Arabs took down the Byzantines and Persians, who were so busy fighting one another to exhaustion that they were unprepared for a fresh onslaught from a more dynamic group of people. But Islam itself could hardly have been spread by conquest; the conquering armies were much, much too small to enforce such a young faith over the very well-established religions of Byzantium and Persia. In fact, the newly subject populations, being "Peoples of the Book," were allowed to keep their respective faiths subject only to certain restrictions (like paying special taxes and being unable to build a church or temple higher than a mosque). Only gradually did these populations convert to Islam, and then only because the new faith seems to have offered them a message lacking in their established traditions. Significantly, Islam was spread to sub-Saharan Africa and Indonesia (where more Muslims live than anywhere else) via commercial contacts, not warfare: people chose this religion willingly more often than they did not.
If you want to hear about warfare and forced conversions, then check out Christianity, which was confined to the urban centers of the Mediterranean basin for centuries until Germanic warrior kings, setting up their own polities on the ruins of the Roman Empire, started forcing their subjects to convert (a task made easier, again, by the relative intellectual sophistication of Christianity as compared to their own pagan traditions). Often these warlords themselves were only converted spontaneously, in the heat of a losing battle, and considered Christianity a kind of magic that would help them keep winning their wars.
I also feel compelled to point out that the Mongol hordes did not exist as such until the thirteenth century, long after the Islamic world had fractured into multiple distinct and autonomous polities.
But you are dead on about Wahabbism, which if you ask me is the greatest problem facing Islam, internally, in this day and age. The difficulty isn't just that Wahabbism is a backwards and skewed interpretation of Islam, it's that the Saudi Royal family believes in it. America is no more to blame for the creation of this monster than sport shooters are to blame for the handgun industry: the responsibility lies on the shoulders of the corrupt fundamentalist despots descended from Ibn Saud. Replace them with progressive, enlightened Islamic governments and the problem will go away.
