I will answer questions #2 and 6 here since both have to do with similar topics.
To say that the Catholic Church claims always to be correct is somewhat unfair. I assume that this question is based on the doctrine of papal infallibility. However, the fact that the Church holds that the Pope is infallible in certain, very limited circumstances, does not mean that the Pope is always infallible, let alone that the Church cannot make mistakes. For example, the Church has only claimed to be issuing an infallible statement about doctrine twice in the past 140 years or so. These statements have only to do with basic doctrines (the Assumption of Mary, the idea that only men can become priests), not with lesser things.
Therefore, it is not surprising that the Church needed to be reformed at times. It is a fallible organization like any other. No organization ever thinks it is doing the wrong thing and continues to do it. But every now and then, organizations come to realize that they have been making mistakes without realizing it and they change. This was true of the Catholic Church in the Middle Ages.
The fact that the Church can sometimes be wrong is illustrated in the Avignon Papacy. This was a period of about 70 years in the 1300s when the popes reigned from Avignon, in France, rather than from Rome. During this time, the popes were more or less controlled by the French kings. This was significant mainly because it led to the Western Schism. This occurred when Pope Gregory XI moved back to Rome and a new pope was elected in Avignon. During this time, there were two (and, for a while, three) men claiming to be pope.
The Avignon Papacy and the schism are important because they led many people to lose faith in the Church because it was so clearly lacking in moral leadership at the highest levels. They also caused popes to lose moral authority, thus making it harder for them to try to claim that they should have any power over secular kings.