This list of questions was excerpted from Answering Islam.org. Which has good resources for understanding the Muslim view of Christianity, and being equipped to answer objections. Most of the site's resources are available in multiple languages.
1. When exactly do you believe that the Bible was corrupted and by whom?
This question is important because it is actually quite easy to demonstrate to a Muslim that when Muhammad recited the Qur'an, he made clear statements which show that he did not believe that the Bible was corrupt at that time. The Qur'an calls on Christians to adhere to the Scriptures that they possessed. There are also verses in the Qur'an which state that John the Baptist and Jesus were taught the Torah by Allah. If this is the case, then the Torah was still intact (according to the Qur'an) during the first century. Add to this the fact that we have in our possession the Dead Sea Scrolls and the Septuagint which predate John and Jesus' birth by some 200 years. Thus it is easy to demonstrate (for anyone who is willing to examine the facts) that according to the Islamic worldview and the manuscript evidence, it is impossible for the Bible to have been corrupted. The logical questions go on and on here. See:
Another one of my favorites is a question which revolves around the false Muslim notion that the incarnation (the ultimate demonstration of God's love for us -- particularly as it culminated in the crucifixion) somehow diminishes God's "greatness". So my question here is something along this line...
2. Philosophically speaking, which is greater, a God who demonstrates his love to the utmost extent (see Philippians 2) or one who refrains from doing so in order to preserve his image of "greatness"?
When we begin to see the world through a Muslim's eyes, and understand their perspective toward the incarnation and the redemptive work of Jesus Christ, and when we imagine a world without the incarnation, it is like having a "It's a Wonderful Life" (Jimmy Stuart movie) experience. We begin to see what an awesome thing the incarnation is, and we appreciate more then ever before what God has done for us! It is my belief that when Muslims are able to see this fact (that true greatness is found with the one who loves the most), then they begin to see the superiority emotionally and philosophically of the Biblical concept of God over the Islamic concept of God. See also the story that is told about the two fathers in this response: www.answering-islam.org/Emails/trinity-where.htm
Another question that one might ask a Muslim would be:
3. If you claim to be born without a sin nature (an inborn propensity toward sin rather than a natural propensity toward righteousness), then how long can you go without sinning? Can you go for a week without sin? How about a day? If you are born basically good, then why does one need to struggle and make a conscious effort to be good and not need to struggle to be bad? Why do we naturally drift toward selfishness and not righteousness?
See a great discussion that covers this and a whole lot more here: www.answering-islam.org/Intro/discussion.pdf
A fourth question might be: Would you be willing to pray with an honest heart and ask God to guide you to His truth, even if that truth is found in the Bible and not in Islam?