Pay special attention to the appendix. This short section offers a concise account of what Christianity is to Kierkegaard. For Kierkegaard, Christ's teachings are absurd from any rational standpoint. Why would an almighty God take any interest in a puny human being? How can a puny human being have a relationship with God? Christianity defies rational understanding. Nevertheless, for Kierkegaard, Christianity is the greatest truth there is, and Christian faith is the highest form of human life, the only form that avoids despair. (Note that the definition of faith at the end of Chapter 1 is essentially identical to the definition of being free from despair that is given at the end of Part I.A.a.)
Kierkegaard's understanding of Christianity creates something of a paradox for us in trying to understand his writings. The Sickness Unto Death seems to be arguing that all people are in despair unless they have faith. If this isn't an argument in favor of Christian faith, then what is it? If Christianity defies understanding and explanation, then what is Kierkegaard up to in his books?
Kierkegaard clearly had strong views about what it means to be a Christian. Maybe he presumed that his Christian readers would be interested in his unique views on their religion. Maybe he was writing just in case there was someone out there who could be helped by his ideas about God. Maybe he didn't really care what everyone else thought of his "absurd" ideas. Or maybe he was trying to show us that rational investigation cannot answer all questions. (See the Overall Analysis and the commentary to Part I.A. for more on this interpretation of Kierkegaard.)
Kierkegaard was an unusual philosopher and his works pose unusual challenges for the reader. There is no final word on how we should respond to his work. As you consider these questions, you may want to consider the long second paragraph of Part II.A. Kierkegaard may be referring to himself when he describes the "poet" who is able to describe religious truth even though he does not live the perfect religious life.