I'm very glad that you have asked these questions, as I really want Muslims and Christians to understand each other
Before I answer, I'll just give a brief bit of context...
When Jesus was born, the main religious text was what we now call the Old Testament (which is currently part of the Bible) as well as some other books with specifications as to the various ceremonies etc. No amount of paper and ink could completely lay out the full meaning of the Old Testament, but the basic storyline is that God created the World etc., but that humans began to sin, which created a barrier between us and God, that He raised up a people to follow Him (these were the Jews), and that, through many prophets, He not only dealt with the issues of the time, but with many similar issues which have followed ever since, at the same time as speaking of a time when one would come who could bridge the gap between God and Man. Finally, the time came, and Jesus came to earth in the form of a humble man (hence being born in a stable, etc.). Others were able to relate to Him because He underwent the same suffering as everyone else, and yet He also was gifted with divine knowledge, and taught in the synagogues. He told many parables etc., but also spoke about how the Son of Man must die. Nobody understood Him. He also healed a great many people, and showed the people many signs and wonders. Then, the Pharisees became jealous, and plotted against Him, resulting in His death. Note that, when He was on the cross, the crowd mocked Him: "If you are truly the Son of God, why don't you set yourself free?" They were the same people who thought that redemption meant redemption from the Romans, not redemption for the soul. However, God's plan was more complex and wonderful than we simple-minded humans could have supposed. Jesus not only died a sacrifice, but rose, as a symbol of God's greatness and mercy. In this way, there was a full circle: Sin through Adam, resulting in separation from God; sacrifice through Jesus, resulting in a reunion with God.
The reason there are many different stories is that, since the Good News spread among not only the Jews but also the Gentiles, some people mixed up the true story with additions from their own past religions, etc. Also, it is because being a Christian requires dedication from the heart, not just actions, so many people who wanted to be powerful (note that, for a large part of history, the most powerful "organisation" or call it what you will in Europe, was the Church) became important "Christians", when all they wanted was power! This obviously corrupted the system, but not beyond repair: thanks to God, it is a fully living religion. But that's my answer to that question.
Like I have mentioned before, the cross is such an important symbol for us bc it represents Jesus' intense love for us, and our redemption: it is a kind of "second chance". Another sign of God's mercy
While it is v important to us to spread the Good News (and good news we believe it to be!), the Bible says that, even if a person's stronghold (those s/he has brought to Christ, etc.) falls, while it will mean that s/he is a lesser person in Heaven, s/he will still have redemption, so yes, the most important thing is to love God with all our heart, soul, mind and strength, and to believe that Jesus came to offer us the precious gift of redemption.
I hope that clears everything up for you, and may Muslims and Christians come to have an understanding between each other!