Chcę się dowiedzieć, gdzie jest książka.

Chcę means I want.

It is the 1st person singular form of the verb chcieć (to want).

A few useful forms:

• chcę = I want
• chcesz = you want
• chce = he/she/it wants
• chcemy = we want
• chcecie = you all want
• chcą = they want

So Chcę się dowiedzieć... literally starts as I want to find out...

Because dowiedzieć się is a fixed verb expression meaning to find out / to learn / to come to know.

In Polish, some verbs regularly appear with się, and you often need to learn them as a whole unit:

• uczyć się = to study / to learn
• bać się = to be afraid
• dowiedzieć się = to find out

So here, się is not optional.
You should think of the whole verb as:

dowiedzieć się = to find out

Because wiedzieć means to know, while dowiedzieć się means to find out or to get to know some information.

That is an important difference:

• wiedzieć = to already know
• dowiedzieć się = to learn/find out something you do not know yet

So:

• Chcę wiedzieć, gdzie jest książka. = I want to know where the book is.
• Chcę się dowiedzieć, gdzie jest książka. = I want to find out where the book is.

Both can work, but they are not exactly the same in meaning.

Yes. Functionally, you should treat dowiedzieć się as one verb.

Polish often writes się separately, but it still belongs to the verb. So although the sentence looks like it has two separate words, learners should memorize:

dowiedzieć się = to find out

Also, the position of się can sometimes move:

• Chcę się dowiedzieć...
• Chcę dowiedzieć się...

Both are possible, though Chcę się dowiedzieć... sounds very natural.

Here dowiedzieć się is an infinitive, because it follows chcę.

The pattern is:

chcę + infinitive = I want to + verb

So:

• Chcę czytać. = I want to read.
• Chcę iść. = I want to go.
• Chcę się dowiedzieć. = I want to find out.

This is very similar to English in structure.

Dowiedzieć się is perfective.

That makes sense because finding out is seen as a completed result: first you do not know, then you learn the information.

Its imperfective partner is usually dowiadywać się.

Compare:

• dowiedzieć się = to find out, successfully learn something once, with a result
• dowiadywać się = to be finding out / to find out repeatedly / in a more ongoing sense

In your sentence, the perfective verb is natural because the speaker wants the result: to get the information.

Because gdzie jest książka is a subordinate clause: where the book is.

Polish usually places a comma before subordinate clauses introduced by words like:

• że = that
• czy = whether/if
• gdzie = where
• kiedy = when
• jak = how

So:

• Wiem, że przyjdzie.
• Nie wiem, gdzie mieszka.
• Chcę się dowiedzieć, gdzie jest książka.

That comma is standard and important in written Polish.

Because this is the normal Polish word order for where is the book? / where the book is.

The basic structure is:

• gdzie = where
• jest = is
• książka = the book / book

So:

• Gdzie jest książka? = Where is the book?
• ...gdzie jest książka. = ...where the book is.

Polish word order is more flexible than English, but gdzie jest książka is the most neutral and natural order here.

Because książka is the subject of jest.

In gdzie jest książka, the book is the thing that is somewhere, so it stays in the nominative:

• książka = nominative singular

If you are asking where something is, the thing itself is often nominative:

• Gdzie jest dom? = Where is the house?
• Gdzie jest samochód? = Where is the car?
• Gdzie jest książka? = Where is the book?

The location itself, if expressed, would usually take a different case after a preposition:

• Książka jest na stole. = The book is on the table. Here stole is locative after na.

It can mean either, depending on context.

Polish has no articles like a and the, so książka can mean:

• a book
• the book

In your sentence, English usually translates it as the book because the speaker probably has a specific book in mind:

Chcę się dowiedzieć, gdzie jest książka.
= I want to find out where the book is.

But Polish itself does not mark that difference with an article.

Yes, it is grammatically correct and natural.

It sounds a bit more deliberate or formal than a very casual everyday sentence, because chcę się dowiedzieć has the feeling of I want to find out rather than simply I want to know.

Depending on context, a speaker might also say:

• Chcę wiedzieć, gdzie jest książka. = I want to know where the book is.
• Chcę sprawdzić, gdzie jest książka. = I want to check where the book is.
• Muszę się dowiedzieć, gdzie jest książka. = I need to find out where the book is.

So your sentence is fine; it just has a specific nuance.

Yes. That is also correct.

Both are natural:

• Chcę się dowiedzieć, gdzie jest książka.
• Chcę dowiedzieć się, gdzie jest książka.

The difference is mainly word order and rhythm, not meaning.
In everyday speech, both are common.

Learners should know that się can move around in many sentences, but not absolutely anywhere.

A rough pronunciation guide:

• Chcę ≈ h-tseh
• się ≈ shyeng or sheng (very rough)
• dowiedzieć ≈ doh-vyeh-jyech
• gdzie ≈ g-jeh (with a soft g/dj-like start)
• jest ≈ yest
• książka ≈ kshyonsh-ka

A few key points:

• ch in Polish sounds like a hard h
• ę is a nasal vowel
• dz / dzie can sound soft and tricky for English speakers
• książka begins with a consonant cluster that takes practice

You do not need perfect pronunciation immediately, but chcę, się, and książka are especially worth practicing.

The direct question would be:

Gdzie jest książka? = Where is the book?

Your original sentence contains that idea as an embedded clause:

• direct question: Gdzie jest książka?
• embedded clause: ..., gdzie jest książka.

This is very similar to English:

• Where is the book?
• I want to find out where the book is.

Notice that Polish does not change the word order in the embedded clause the way English does. It stays:

• gdzie jest książka

not something like gdzie książka jest, unless you want a marked or special emphasis.