Was Muhammed a false prophet? If so, is the religion of Islam also false?

In order to be a prophet, you must be able to "tell of things to come." What actually did he predict? Apparently, "Allah" revealed things into him and it was put into the Qu'ran. It was actually spread AFTER he died across the Middle East. Also, Islam says that Jesus was simply a "prophet" and not the son of God. Muslims seem to think he was no more important than Abraham and Moses. But Jesus said there would be no "great prophet" after him, and said to be aware of "false prophets." Did Muhammed simply "borrow" things from the Christian Bible and put it into the Qu'ran? Islam says that Judaism and Christianity "messed up" God's word, yet BOTH religions are much older than Islam. Not that their beliefs are false, but is the religion itself false? And why is Islam even that appealing to so many people? Wouldn't it be difficult to covert from Christianity (Jesus) to Islam (Allah, Muhammed)? The Bible speaks of Judaism AND Christianity, but not Islam. And since Christianity is the dominant religion, I thought the question was interesting. One more thing: Jesus said the only way to his father is THROUGH him. What do Muslims think of this since they don't think Jesus died for man's sins?