Ich bringe das Buch morgen in die Bibliothek zurück.

Because zurückbringen is a separable verb.

• The full infinitive is zurückbringen = to bring back / to return
• In a normal present-tense main clause, the verb splits:
  • Ich bringe ... zurück.
• The conjugated part (bringe) goes to the usual verb position.
• The prefix (zurück) goes to the end.

Compare:

• Ich bringe das Buch zurück.
• Ich will das Buch zurückbringen.
  In this case, the verb does not split because zurückbringen stays as an infinitive at the end.

Because the subject is Ich (I), and the verb bringen has to be conjugated to match it.

Present tense of bringen:

• ich bringe
• du bringst
• er/sie/es bringt
• wir bringen
• ihr bringt
• sie/Sie bringen

So Ich bringe means I bring or, in this context, I am bringing / I will bring.

German very often uses the present tense for the future when the time is already clear.

Here, morgen already tells you the action is in the future, so Ich bringe ... morgen ... zurück is completely natural.

German could also say:

• Ich werde das Buch morgen in die Bibliothek zurückbringen.

But that future form is often unnecessary unless the speaker wants to emphasize the future, make a prediction, or sound more formal.

Das Buch is the direct object of the sentence: it is the thing being brought back.

The verb bringen usually takes an accusative object, so the book is in the accusative case.

For das Buch, nominative and accusative look the same:

• nominative: das Buch
• accusative: das Buch

So the form does not change, even though the grammatical role does.

Because in is a two-way preposition:

• it takes accusative when there is movement toward/into a place
• it takes dative when there is location in a place

Here, the book is being taken into the library, so German uses the accusative:

• in die Bibliothek = into the library

Compare:

• Ich bringe das Buch in die Bibliothek.
  movement into the library
• Das Buch ist in der Bibliothek.
  the book is in the library

German main clauses usually put the conjugated verb in second position. That explains bringe.

After that, German is more flexible than English, but there are common patterns. In this sentence:

• Ich = subject
• bringe = conjugated verb
• das Buch = object
• morgen = time
• in die Bibliothek = place/direction
• zurück = separable prefix at the end

A very common order is:

• subject + verb + object + time + place + separable prefix

So this sentence sounds natural and standard.

Yes. German word order is flexible, as long as the verb placement rules are respected.

For example, all of these are possible:

• Ich bringe das Buch morgen in die Bibliothek zurück.
• Morgen bringe ich das Buch in die Bibliothek zurück.
• Ich bringe morgen das Buch in die Bibliothek zurück.

The first one is neutral and natural.
If you put morgen first, you emphasize tomorrow a little more.

Remember: in a main clause, the conjugated verb still has to stay in second position:

• Morgen bringe ich ...
• not Morgen ich bringe ...

Zurück usually means back.

In zurückbringen, it gives the idea of bringing something back.

You will see zurück in many other separable verbs too:

• zurückkommen = to come back
• zurückgehen = to go back
• zurückgeben = to give back
• zurückschicken = to send back

So if you recognize zurück, it often signals some idea of returning.

Both can mean to return something, but they are used a little differently.

• zurückbringen = to bring something back
  This emphasizes physically taking it back somewhere.
• zurückgeben = to give something back / return something
  This is often more general.

In your sentence, zurückbringen works very well because the speaker is physically taking the book back to the library.

Examples:

• Ich bringe das Buch in die Bibliothek zurück.
  I’m bringing the book back to the library.
• Ich gebe dir dein Geld zurück.
  I’m giving your money back to you.

Because in die Bibliothek suggests movement into the library building / inside the library, which is a natural way to say you are returning a book there.

• in die Bibliothek = into the library
• zur Bibliothek = to the library

Zur Bibliothek can sound more like movement in the direction of the library or up to it, rather than specifically going inside. In this context, in die Bibliothek is the more natural choice.

Yes. Like English, the German present tense can cover more than one idea depending on context.

This sentence can naturally be understood as:

• I bring the book back tomorrow
• I am bringing the book back tomorrow
• I will bring the book back tomorrow

Since morgen makes the future clear, German does not need a special future form here.

Usually yes, but learners sometimes confuse Bibliothek with Bücherei.

• Bibliothek is the standard word for library
• Bücherei also means library, but can sound a bit more old-fashioned or can refer especially to a lending library in some contexts

In modern standard German, Bibliothek is very common and completely normal here.

Only in certain structures.

In a normal main clause, the separable verb splits:

• Ich bringe das Buch zurück.

But in some other structures, the full infinitive zurückbringen stays together:

• Ich will das Buch zurückbringen.
• Ich werde das Buch morgen in die Bibliothek zurückbringen.
• ..., weil ich das Buch morgen in die Bibliothek zurückbringe.
  In a subordinate clause, the conjugated verb goes to the end, but the prefix still belongs with it in the written form.

So whether it splits depends on the sentence structure.