Do Catholics believe everything in the bible is true as written?

Within most denominations including the Catholic Church, there are some who believe in a literal interpretation of creation and the flood, and some who don't.

As stated in Geremia's answer, the Catholic Church teaches,

The first three Chapters of Genesis contain narratives that correspond to objectively real and historically true events, no myths, no mere allegories or symbols of religious truths, no legends.

1909 Pontifical Biblical Commission (Latin original)

but Pope Francis says:

[God] created beings and allowed them to develop according to the internal laws that he gave to each one, so that they were able to develop and to arrive and their fullness of being... And so creation continued for centuries and centuries, millennia and millennia, until it became which we know today, precisely because God is not a demiurge or a magician, but the creator who gives being to all things...

"Francis inaugurates bust of Benedict, emphasizes unity of faith, science". cna. 27 October 2014. Retrieved 3 November 2014.

So it is not clear as to what is the official position of the Catholic Church on this.

Most people have a kind of hybrid belief. They take some things of the Bible as literal and some as figurative. Taking certain writings as figurative is fine when the Bible is explicit that it is figurative. Some of these include prophecy and parables. Nevertheless, the Bible tells the account of creation, Noah, and Jonah as real, literal, historic events.

For instance, the great majority of Christians believe in the story of Jesus as it is written in the Bible. In fact, I don't know any Christian who doesn't, though there may be some. However, in the Bible Jesus talks about Noah as a literal person that lived in an actual time and went through a world wide flood.

37 But as the days of Noah were, so also will the coming of the Son of Man be. 38 For as in the days before the flood, they were eating and drinking, marrying and giving in marriage, until the day that Noah entered the ark, 39 and did not know until the flood came and took them all away, so also will the coming of the Son of Man be.

Matthew 24:37-39

This is problematic because if Jesus is real, and God, why would He refer to Noah and the time of Noah as real, if it was simply figurative?

Jesus says the same of Jonah:

For as Jonas was three days and three nights in the whale's belly; so shall the Son of man be three days and three nights in the heart of the earth.

Matthew 12:40

In other words, if Jonah did NOT spend 3 days and 3 nights in the belly of the whale, because you don't believe it happened, then neither did Jesus spend three days and three nights in the heart of the earth.

In this light, a hybrid belief in the Bible doesn't make sense. Either you believe the Bible is all fairy tale, or the Bible is all real and true. It either happened or it didn't, there is no middle ground here. Either the Bible is, like it claims, the word of God, or it is not. Just really can't have it both ways, if you want to be consistent.

OP asks:

Do Catholics believe everything in the bible is true as written?

<meme>You keep using that word, "true". It does not mean what you think it means.</meme>

The short answer is "Yes, and not quite", if by "true" is intended a flatly literalistic understanding of everything written in the Bible. (On the problem of "literalism", not restricted to Catholic interpretation of Scripture, see James Barr, "Literality", Faith and Philosophy 6(4) (1989): 412-428.)

Dei Verbum

A good way to get a handle on Catholic understanding of Scripture is to read the document from the Second Vatican Council (which met throughout 1962-1965) entitled Dei Verbum (which also has a helpful article on Wikipedia). That document both affirms that

the books of Scripture must be acknowledged as teaching solidly, faithfully and without error that truth which God wanted put into sacred writings for the sake of salvation (Ch. III ¶ 11).

It also immediately goes on to acknowledge that

since God speaks in Sacred Scripture through men in human fashion, the interpreter of Sacred Scripture, in order to see clearly what God wanted to communicate to us, should carefully investigate what meaning the sacred writers really intended, and what God wanted to manifest by means of their words" (Ch. III ¶ 12).

[Emphasis added by me.] In practice, then, one needs to consult approved teachers of the church to know in any particular case whether such-and-such a case is to be taken as literally true. (And the church has a teaching office in this regard: "It devolves on sacred bishops 'who have the apostolic teaching' to give the faithful entrusted to them suitable instruction in the right use of the divine books, especially the New Testament and above all the Gospels" [Dei Verbum, Ch. VI ¶ 25].)

Examples

OP gives two examples: "...Noah actually having 2 of every animal on one ark, Jonah living inside of a whale...". Between them, they suggest the scope of possibilities open to Catholic "belief" about the Bible, as displayed by the Jerome Biblical Commentary, published in the wake of Vatican II, and having the nihil obstat (explanation) and imprimatur (also explained):

1. Noah - The article on Genesis describes its stories as "history", but in a heavily qualified way, since this "history" has a divine origin, purpose, and unity:

   Because it is supernatural, the purpose is beyond the effective control of modern scientific history. Therefore, the ultimate meaning of Genesis, like that of the other books of the Bible, will always elude the historian who works outside its religious postulates. (p. 8)

   Meanwhile, the events of the "primitive history" (Genesis 1-11) are "facts", "events of a cosmic order that affected universal man", so that the "first 11 chapters of Genesis present truths based on historical facts" (p. 8). In practice, for the flood story, the composite nature of the biblical account -- made up of material from "J" and "P" -- is a given, and the source of the story found in Mesopotamian flood accounts, with parallels noted and discussed: "The non-biblical versions reflect pagan mythology... In the biblical story, the one God, supreme lord of the situation, decrees the flood because of man's sin" (p. 15). The "cosmic" nature of the whole story is repeatedly stressed.

   There is no special consideration given as to the pairs of animals (6:20; nor the tension with there also being "seven pairs" instructed in 7:2-3).

2. Jonah - is taken to be a product of the period 400-200 BC (p. 633; and roughly Hellenistic, then), and asserts

   Although scholars differ as to the term that should be used in determining the literary form of Jonah, they would agree that the book is not to be classified as history. ... Jonah is to be classified as a didactic narrative, satirical in tone with a profound theological purpose. (p. 634)

Conclusion

Hopefully this makes clear how it is that Catholic teaching affirms that the Bible is true, but that at the same time, this is not to be understood in terms of taking all its statements "literally".

St. Thomas Aquinas writes in Summa Theologica I q. 1 a. 10 ("Whether in Holy Scripture a word may have several senses?"):

all the senses [of Holy Scriptures]* are founded on one—the literal

^{*Which are (ibid. arg. 1): "historical or literal, allegorical, tropological or moral, and anagogical"}

If the foundation of all the other senses are falsities (lies), then the assertions of Holy Scriptures based on them would also be falsities (lies). How can truth come from falsehood except accidentally?

The prophecies and miracles set forth and recorded in the Sacred Scriptures are the fiction of poets, and the mysteries of the Christian faith the result of philosophical investigations. In the books of the Old and the New Testament there are contained mythical inventions…

cf. the magisterial quotes here on inerrancy

The Catholic Church teaches, in the decisions of the 1909 Pontifical Biblical Commission (Latin original), that at least

The first three Chapters of Genesis contain narratives that correspond to objectively real and historically true events (rerum vere gestarum narrationes quae scilicet obiectivae realitati et historicae veritati respondeant), no myths, no mere allegories or symbols of religious truths, no legends.

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