From the Christian paradigm, I don’t think Christians are looking for a prophet, in the Old Testament sense. What is interesting about Jesus is that he did NOT bring a new scripture, a new holy book.
Jesus brought the Holy Spirit to everybody, it seems to me, that he wanted to make everybody a prophet (based on the teachings of the Orthodox Church), and if one read the new testament (a scripture that Jesus did NOT bring), this seem very likely.
In terms of Jesus being God, this would be a matter of debate. The disciples of Jesus, of which there were many, some of them believed Jesus to be God, while others did not see Jesus to be God. The Orthodox Church, didn’t want to exclude any of the disciples, formulated a creed which included all of them, that Jesus is 100% man and 100% God. But one has to realize it wasn’t a consensus among the disciples of Jesus. I think part of the confusion that existed among the disciples, were they had different backgrounds, some of jewish origins and others of pagan origins. So depending on your background, determines how you understood what Jesus said. The Jewish population by large did not see Jesus as God, it was the pagan disciples who converted to Christianity that saw him as God.
So from one perspective, Islam does fit into the Christian paradigm, just not the Orthodox/Cathoic paradigm, who chose to embrace both groups of the disciples of Jesus. While Islam only embracing one group of the disciples of Jesus, the ones who did not see Jesus as God.