Does the Catholic Church have a fixed list of doctrines you must believe to be saved?

To a certain extent that is true, but we have things that compensate. One is canon law, a big thick book that tells you what you can or cannot do. Then you have the catechism, and sometimes catechisms are very doctrinaire, like the Council of Trent catechism, which was made purposely to enumerate and categorize the doctrines that came out of Trent; the current catechism is written more like prose and is not as detailed. Then you have Ludwig Ott's Fundamentals of Catholic Dogma, a great book that lists all the major categories of doctrine with the Fathers who held them and the Scripture passages. You have the William Jurgens three-volume set of quotes from the early Fathers on almost every doctrine, which any layperson can use. And for the serious student, there are hundreds of volumes of the Fathers and the medievals in the original languages. So while there is no single hundred-item list published by the Vatican itself, we have more than enough, scattered across these sources and even on the Vatican website, to compensate for it.