According to Catholicism which parts of the Bible actually happened historically?

The entire New Testament (sans Revelation because it is obviously metaphorical in many ways) is considered to be fully historical. The Old Testament is read historically from Exodus and onwards, besides maybe Job or Tobit. The Church has no official teachings on the historicity of Genesis, but the past three popes and many of the saints (such as Aquinas and Augustine) have believed in a metaphorical approach to the creation story, the flood, and Babel.

The Catholic Church Magisterium has not committed to reading the first few chapters of Genesis (from Adam to Noah, at least) as historical / scientific account. Instead, both the Catholic Church and a growing segment of Protestants and Evangelicals, emphasize that scientific truth and the theological truth are compatible with each other. What has to be taken by faith is what those first chapters teach us about God's nature and our nature, and the Church Magisterium has the authority to interpret them accordingly.

The solution: identifying the genre of the Creation story, Adam and Eve, and the Flood story as theological truth cast in ancient Hebrew cosmology which in turn adopts elements of other mythologies of the Ancient Near East. Thus, we notice similarities of the Creation Story to Enûma Eliš and the Noah Story to the Epic of Gilgamesh. For example, this article shows some parallels.

The Hebrew author of Genesis thus was countering the theology embedded in the Mesopotamian myths by recasting the story in terms of Hebrew theology. In Hebrew theology, the True and Real God of the Universe (who also is the Personal God who chose Israel as His special people) created human being as His Imager In the World. Notice the big contrast to the Babylonian myth where their gods created human beings to be slaves for the gods. In the Hebrew author's hand, the story thus highly "upgraded" the status of human beings, and that's one of the key point of the Hebrew theology. (Note: see LBD entry on 'image of God' why the functional 'God's imager' is a better translation.)

Some quotes from a Catholic apologetics website article How to Read the First Chapter of Genesis quoting Pope John Paul II, Pope, Leo XIII, Pope Pius XII, and St. Augustine (emphasis mine):

The confusion over this issue, which Pope John Paul II addressed in 1996 in his highly publicized letter about evolution, boils down to the question of how to read the biblical creation account. In his letter, John Paul simply reiterated what the Magisterium has argued tirelessly since Leo XIII's Providentissimus Deus (1893): The author of Genesis did not intend to provide a scientific explanation of how God created the world. Unfortunately there are still biblical fundamentalists, Catholic and Protestant, who do not embrace this point.

When Christ said that the mustard seed was the smallest of seeds — and it is about the size of a speck of dust — He was not laying down a principle of botany. In fact, botanists tell us there are smaller seeds. Our Lord was simply talking to the men of His time in their own language, and with reference to their own experience. Similarly, the Hebrew word for "day" used in Genesis ("yom") can mean a 24-hour day, or a longer period. Hence the warning of Pius XII in Divino Afflante Spiritu (1943), that the true sense of a biblical passage is not always obvious. The sacred authors wrote in the idioms of their time and place.

As Catholics, we must believe that every word of Scripture is inspired by the Holy Spirit, a claim the Church will not make even for her infallible pronouncements. However, we must not imagine the biblical authors as going into a trance and taking automatic dictation in a "pure" language untouched by historical contingency. Rather, God made full use of the writers habits of mind and expression. It's the old mystery of grace and free will.

A modern reader of Genesis must bear in mind the principles of biblical exegesis laid down by St. Augustine in his great work De Genesi Ad Litteram (On the Literal Interpretation of Genesis). Augustine taught that whenever reason established with certainty a fact about the physical world, seemingly contrary statements in the Bible must be interpreted accordingly. He opposed the idea of a "Christian account" of natural phenomena in opposition to what could be known by science. He viewed such accounts as "most deplorable and harmful, and to be avoided at any cost," because on hearing them the non-believer "could hardly hold his laughter on seeing, as the saying goes, the error rise sky-high."

But the Magisterium did clarify the boundaries of acceptable position in this Catholic Answers article Adam, Eve, and Evolution, specifically ruling that "the human race have to descend from an original pair of two human beings" to preserve the doctrine of original sin:

In this regard, Pope Pius XII stated: “When, however, there is question of another conjectural opinion, namely polygenism, the children of the Church by no means enjoy such liberty. For the faithful cannot embrace that opinion which maintains either that after Adam there existed on this earth true men who did not take their origin through natural generation from him as from the first parents of all, or that Adam represents a certain number of first parents. Now, it is in no way apparent how such an opinion can be reconciled that which the sources of revealed truth and the documents of the teaching authority of the Church proposed with regard to original sin which proceeds from a sin actually committed by an individual Adam in which through generation is passed onto all and is in everyone as his own” (Humani Generis 37).