The Ottomans had skilled soldiers, so over time they would conquer different parts slowly, and once they had defeated the last of the Byzantine Empire, the Ottoman Empire was now a large empire. The Ottoman Empire started off as a little community, but kept growing into a large empire, lead by a man named Osman.
Not by a long shot. The rulers of the Ottoman Empire were the Sultan, in political matters, and the Caliph, in spiritual matters. Shiites (shia) are a sect of Islam vigorously opposed by the Ottoman Empire and were often seen as a fifth column with loyalties to the Ottoman Empire's rival: the Safavid Persian Empire.
None. Muhammad died long before the rise of the Ottoman empire. If you mean Mehmed the Second, one of the sultans of the Ottoman empire, he was the one who conquered Constantinople and made it the new capital; renamed Istanbul. He expanded the empire to cover almost all of Serbia as well as including Anatolia & the Crimea.