The prophets came after Moses and foretold of the Messiah. Christians see fulfillment of these prophecies in Jesus Christ. There are no prophecies for Islam to fulfill as the only prophecies made in the New Testament deal with the end times, not a future prophet.
And no, most Israelites did not become Christians, and most Christians did not become Muslims. Where on Earth did you get your info?
Good census data for the period 1 AD to 700 AD is hard to come by. Just the same, there was once a time that most of them that considered the Ten Commandments to be sacred were Jews, and later most of those guys were Christians. I realize that some say a Jew is not a Christian and a Christian is not a Jew. I'd argue that you can't be true to the Torah and deny Christ, and that to be a Christian you can't just chuck the old Testament. Sort of like "If you believed Moses, you would believe me, for he wrote about me".
During the first half millennium, there were five major cities with bishops- Rome, Constantinople, Antioch, Jerusalem, and Alexandria. All but one spoke Greek (the language of the Gospels) and Latin was the home language of just the Roman church. Since then, four out of five went for Islam. Of course, during the past half millennium something really deferent's seemed to have happened that's changed everything, but I digress.