Are Daniel chapters 13 and 14 (Susanna, and Bel and the Dragon) really part of inspired Scripture?

Yes. Daniel 13 and 14, the chapters known as Susanna and Bel and the Dragon, are genuinely part of the canon of Scripture. That they survive in Greek rather than Hebrew does not count against them. Yes, they are Scripture. These are the sections that go by the names Susanna, which is Daniel 13, and Bel and the Dragon, which is Daniel 14. Some manuscripts have them in Greek. They are part of the canon all the same. Honestly, I do not think we have to defend this. It is like asking me to defend whether Genesis belongs in the Bible. I do not decide that, and neither do you. It was decided long ago by the Fathers of the Church, led by the Holy Spirit in their councils and affirmed by the popes, and that is how we got the Bible we have. If you can accept the Church's authority for the books you like, you have to accept it for the books you did not know about. But since the objection comes up constantly, let me answer it. The word deuterocanonical means "second canon," and it covers the seven Old Testament books the Protestants call the Apocrypha, along with these portions of Daniel and Esther. Protestants say apocrypha means hidden and uninspired. In the Catholic Church these books were always accepted. The canon was first approved at the Council of Rome in 380 under Pope Damasus, then at Hippo in 393, Carthage in 394, by Pope Innocent I in 405, and again at the Council of Florence. Every subsequent council accepted them. The Council of Trent then issued the first formally infallible decree on the canon and declared that it could not be reformed: no books added, no books taken away. Vatican I ratified the same canon. And notice the point that settles the argument with Protestants: the canon dogmatized at Trent is identical to the canon authorized at Rome, Hippo, Carthage and Florence. Trent did not add anything. It closed the discussion. Now the specific objection about Hebrew. It is not the test. The Church has never held that a book must have a surviving Hebrew original to be inspired; some books of Scripture were originally written in Greek. Augustine went the other way and thought the Septuagint Greek itself was inspired, which is not the Church's position either. The rule is not the language of the manuscript; the rule is the judgment of the Church. Best guesses will never settle what is God's word. If we want an inerrant canon, it can only come from an infallible judge, and God has communicated that judgment through His Church. There is also a history behind the dispute worth knowing. The Palestinian Jews who handed on Genesis through Malachi took great pride in their purely Hebrew culture. After Alexander, the Alexandrian Jews had a broader collection and their Greek translations. When the Jews at Jamnia later settled on the narrower list, they were no longer God's chosen people and no longer the authority over the canon; the Church was, from the beginning. So when Protestants appeal to the Jewish rejection of these books, they are appealing to a decision made by people who had already rejected the Messiah. As for Jerome, whose name always gets thrown at us: yes, he had reservations. But in 382 he submitted to Pope Damasus and the Council of Rome and accepted the deuterocanonicals as Scripture. That is not an argument against the Catholic position; it is an illustration of it, because it shows Jerome's explicit allegiance to the Church as his authority. And reservations were not unique to him. Athanasius opposed the deuterocanonicals and also opposed the book of Esther, which everybody accepts. There were disagreements about the canon right up until the councils confirmed it, exactly as there were disagreements about almost every doctrine until it was defined. Even Cardinal Cajetan, one of our best men, disputed some of these books before Trent, and he was not censured for it, because the Council of Florence had not used the word canon and there was still room for debate. Trent removed the room. One last thing, from experience. When I came into the Church I found these books hard to accept in principle. Then I actually read them. Wisdom and Sirach are among the greatest books I have ever read in the Bible. I would put Wisdom and Sirach up against Proverbs, and Proverbs is very good. Read Daniel 13 and 14 for yourself. Susanna is one of the finest short accounts of false witness and God's vindication of the innocent anywhere in Scripture, and Bel and the Dragon is a demolition of idolatry that has not aged a day.