This post continues my series of short answers to common questions about Catholicism. For the previous parts in the series, see the "Catholic Q-A Series" blog label.
What are some examples of sins against the Holy Spirit?
The primary sin against the Holy Spirit is the act of disbelief of the Spirit's divinity and His working in Christ and through the Church. This can also take the form of despair over one's soul, in which a person considers oneself beyond the saving power of the Holy Spirit.
What did Jesus mean when he said that heaven and earth would pass away but his words would last forever? (cf. Mt 24:35)
When Jesus comes again, heaven and earth will pass away. He will usher in a new heaven and a new earth, in which all evil, and sin, and suffering, and weakness, and temptation, and hunger, and every ill-effect of sin and the devil on earth will be definitively destroyed. On that day, heaven and earth will come together to be one place of perfect peace and happiness where Jesus reigns forever and ever (cf. Rev 21:1-5). By saying that His words will outlast even the entire created order as we know it, He is emphasizing the permanent relevance and power and timelessness of His word.
I've heard that Jesus could've been as old as a toddler or possibly even older when the three wise men came. Does the Church have an age range established?
The Church usually does not define incidental matters of history like this. So, there is no authoritative teaching on the matter.
When and why did the Orthodox churches branch away? Why is Catholicism broken up? Why wouldn't the pope unite them?
Well, it isn't that Catholicism is broken up, it's that several groups of Christians have separated themselves from Her over the years. There had been many years of theological disputes and hurt feelings between Christians in Western and Eastern Europe leading up to 1054 AD, when representatives from both sides excommunicated each other. This was the "straw that broke the camel's back", so to speak, and was the impetus for many churches in the East to form what would be known as the Eastern Orthodox Church. However, since the Eastern Orthodox Church maintains a valid apostolic succession and all seven sacraments, there are still many ties that bind us. Especially since the Second Vatican Council, the Popes of the Catholic Church and the Patriarchs of the East have made every effort at reunification. I think there is good reason to believe that one day we will be one Body again.