Is the Pope infallible?

Yes, on doctrinal and moral matters officially propagated as binding Christian teaching. Jesus Christ, the founder of the Catholic Church, in appointing the apostle Simon as the first pope, gave him the charism of infallibility, promising him, "Whatsoever you bind upon Earth is bound in Heaven". Apparently it works! His Church remains ONE in belief, ONE in teaching, ONE in worship throughout the world after 2,000 years, while unauthorized manmade religion has fragmented into thousands of conflicting denominations is just a few hundred years. You just can't beat God's plan! Jesus knew you cannot have truth without unity, because conflicting beliefs necessarily mean false beliefs. Truth cannot conflict with truth. He also knew you cannot have unity without genuine authority, which is why He gave Simon the title "Peter", meaning "Rock". and told him he was to be the Rock upon whose authority the Christian Church would be built. He then invested Simon Peter - "Simon the Rock" - with full authority, symbolized by "the keys to the kingdom", the universal symbol of supreme authority; and the charism of infallibility.