Książka jest niedostępna, czyli muszę czekać.

Because it agrees with książka, which is a feminine singular noun.

In Polish, adjectives usually match the noun in:

• gender
• number
• case

Here:

• książka = feminine singular
• so the adjective must also be feminine singular: niedostępna

Compare:

• niedostępny = masculine singular
• niedostępna = feminine singular
• niedostępne = neuter singular / non-masculine plural

So Książka jest niedostępna means literally The book is unavailable, with the adjective matching book grammatically.

Because książka is the nominative singular form, which is the basic dictionary form and is used here as the subject of the sentence.

In Książka jest niedostępna:

• Książka = the subject
• jest niedostępna = what is being said about the subject

If you changed the role of the noun, the case would change:

• Widzę książkę. = I see the book. → accusative
• Nie ma książki. = There is no book. → genitive

But here the book is simply the thing being described, so nominative is correct.

Czyli often means:

• that is
• in other words
• which means
• sometimes, in context, something close to so

In this sentence:

• Książka jest niedostępna, czyli muszę czekać.

The idea is:

• The book is unavailable, which means I have to wait.

So czyli connects the first statement to its consequence or explanation.

A useful comparison:

• czyli = which means / in other words
• więc = so / therefore

In everyday English, you might translate this whole sentence as:

• The book is unavailable, so I have to wait.

Yes, in many contexts you could say:

• Książka jest niedostępna, więc muszę czekać.

This sounds very natural and may even feel more directly causal:
The book is unavailable, so I have to wait.

The difference is small, but:

• więc focuses more on the result: so / therefore
• czyli often sounds more like: which means / that is to say

So:

• czyli = interpreting the first fact
• więc = giving the consequence

Both are understandable here, but więc is often the more straightforward choice if you want a simple so.

Because in Polish, czyli is normally preceded by a comma when it introduces an explanation, restatement, or conclusion.

So:

• Książka jest niedostępna, czyli muszę czekać.

That comma is standard punctuation.

You will often see the same with similar connectors:

• To mój brat, czyli syn moich rodziców.
• Jest chory, więc zostaje w domu.

Polish uses commas quite regularly before linking words like this.

Because after musieć (to have to / must), Polish uses the infinitive form of the second verb.

So:

• muszę = I have to
• czekać = to wait

Together:

• muszę czekać = I have to wait

This is similar to English:

• I must wait
• not I must am waiting

More examples:

• Muszę iść. = I have to go.
• Muszę pracować. = I have to work.
• Muszę czytać. = I have to read.

Muszę is the 1st person singular present tense form of musieć (to have to / must).

It means:

• I must
• I have to

A few forms of musieć are:

• muszę = I must
• musisz = you must
• musi = he/she/it must
• musimy = we must
• musicie = you must
• muszą = they must

So in this sentence, the speaker is saying:

• I have to wait

In normal standard Polish, jest is usually used in sentences like this.

So:

• Książka jest niedostępna. = The book is unavailable.

Unlike Russian, for example, Polish normally does not drop the present-tense to be in ordinary full sentences.

You may sometimes see omission in:

• notes
• headlines
• informal shorthand
• poetic style

But for a standard learner sentence, jest is the correct and natural form.

Yes, niedostępna works well for unavailable.

It comes from:

• dostępny = available / accessible
• niedostępny = unavailable / inaccessible

Because książka is feminine, it becomes:

• niedostępna

Depending on context, Polish might also use other words:

• wypożyczona = borrowed out / checked out
• brak książki = the book is unavailable / out of stock
• nie ma tej książki = this book isn’t available / there is no copy

But niedostępna is perfectly correct and natural in a broad sense.

Yes. Polish word order is more flexible than English, although each version can sound slightly different in emphasis.

For example:

• Książka jest niedostępna, czyli muszę czekać.
• Muszę czekać, bo książka jest niedostępna.
• Książka jest niedostępna, więc muszę czekać.

These all express roughly the same idea, but:

• starting with Książka jest niedostępna emphasizes the fact about the book
• starting with Muszę czekać emphasizes the speaker’s situation

Polish often allows this kind of reordering more easily than English does.

A rough pronunciation guide:

• książka ≈ kshyonsh-ka
• jest ≈ yest
• niedostępna ≈ nyeh-doh-STEMP-na
• czyli ≈ CHIH-li
• muszę ≈ MOO-sheh
• czekać ≈ CHEH-kach

A few important sound notes:

• ksią- in książka is tricky; the ą is nasal
• sz sounds like English sh
• cz sounds like English ch
• ę in muszę is a nasal vowel, but in normal speech at the end of a word it is often pronounced less strongly than learners expect

You do not need a perfect nasal sound immediately; being consistent and clear matters more at first.

Because czekać is the infinitive form of the verb to wait.

Many Polish infinitives end in:

• -ać
• -ić / -yć
• -eć
• -ować

Examples:

• czekać = to wait
• czytać = to read
• robić = to do/make
• pracować = to work

So after muszę, you use the infinitive:

• muszę czekać = I have to wait

Yes, it is grammatical and understandable.

That said, depending on the exact context, a Polish speaker might also say:

• Książka jest niedostępna, więc muszę czekać.
• Muszę czekać, bo książka jest niedostępna.
• Tej książki teraz nie ma, więc muszę czekać.

Your original sentence is good Polish. The only nuance is that czyli can sound a bit more like which means than plain so, so some speakers might prefer więc in everyday causal speech. But the original sentence is still fine.

Word by word, it is:

• Książka = book
• jest = is
• niedostępna = unavailable
• czyli = which means / so
• muszę = I must / I have to
• czekać = to wait

So the structure is:

• [Subject] + [is] + [adjective], + [connector], + [I have to] + [infinitive]

Very literally:

• Book is unavailable, which means I have to wait.

Natural English:

• The book is unavailable, so I have to wait.