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Yes, Christianity and Islam have many similarities. In fact, they along with Judaism are often referred to as the Abrahamic faiths. These three religions are very closely related in their origins, beliefs, and revealed books, or holy scriptures. They are also closely related in their moral and ethical beliefs, as well as their views of the individual and social life. The three religions also have many differences an example includes their Central prophet. Islam believes that Muhammad is God's chosen prophet while Christianity believes that Jesus is God's central prophet. Jews have a firm believe that Moses is indeed the chosen prophet of God. There are many other similarities and differences; I have enclosed a link to that clearly makes comparisons:

http://www.beliefnet.com/features/abrahamicfaiths....

Yes, quite similar actually. Their holy writings are actually in agreement with each other on many historical points. Islam is inclusive of much of what Christianity holds to be true.

They both worship a higher authority.