Vagon çok kalabalık.

In Turkish, the verb to be is often left out in the present tense when the subject is he/she/it or a noun.

So:

• Vagon çok kalabalık. = The wagon/car is very crowded.

This is completely normal Turkish.

Compare:

• Ben yorgunum. = I am tired.
• Sen yorgunsun. = You are tired.
• Vagon yorgun would not make sense semantically, but grammatically it shows the same pattern: in 3rd person, Turkish often has no separate word for is.

If you want a past meaning, then Turkish does mark it:

• Vagon çok kalabalıktı. = The wagon was very crowded.

Vagon means wagon, railway car, or carriage.

In modern usage, it usually refers to one car of a train, not the whole train.

So depending on context, Vagon çok kalabalık could mean:

• The carriage is very crowded.
• The train car is very crowded.

It does not usually mean the whole train. For the whole train, Turkish would more naturally use tren:

• Tren çok kalabalık. = The train is very crowded.

Turkish does not have a word exactly like English the.

A bare noun like vagon can mean:

• the wagon
• a wagon
• sometimes just wagon(s) in a general sense

The exact meaning depends on context.

If Turkish wants to make the noun clearly indefinite, it can use bir:

• Bir vagon çok kalabalık. = One/A carriage is very crowded.

But in your sentence, vagon by itself is natural and enough.

Here, çok means very.

It comes before an adjective to strengthen it:

• çok kalabalık = very crowded

But çok can also mean much, many, or a lot, depending on the sentence.

Examples:

• Çok güzel. = Very beautiful.
• Çok insan var. = There are many people.
• Onu çok seviyorum. = I love him/her a lot.

So in this sentence, çok is working as an adverb modifying kalabalık.

It can be both, depending on how it is used.

In Vagon çok kalabalık, kalabalık is an adjective, meaning:

• crowded

But kalabalık can also be a noun, meaning:

• crowd
• a lot of people
• a group/gathering

Examples:

• Vagon kalabalık. = The carriage is crowded.
• Büyük bir kalabalık vardı. = There was a big crowd.

So here it is definitely the adjective crowded.

Because in Turkish, when you make a sentence with a noun and an adjective as the predicate, the adjective commonly comes at the end.

Pattern:

• [subject] + [adverb if any] + [adjective]

So:

• Vagon çok kalabalık.

This is similar to saying:

• The carriage very crowded.

with the is understood.

Also, remember that Turkish often puts the main information at the end, so ending with kalabalık sounds very natural.

Yes, but that is not the same sentence.

• Vagon çok kalabalık. = The carriage is very crowded.
  This is a full sentence.

• Çok kalabalık vagon = very crowded carriage
  This is just a noun phrase, not a complete sentence by itself.

So the difference is:

• noun + adjective structure as a sentence: Vagon çok kalabalık
• adjective + noun structure inside a noun phrase: çok kalabalık vagon

Because it is being used as a predicate adjective in the 3rd person singular present tense, where Turkish usually leaves things in the basic dictionary form.

So:

• Vagon kalabalık. = The carriage is crowded.

No extra ending is needed.

But in other persons, Turkish does add endings:

• Ben kalabalık değilim. = I am not crowded (grammatically possible, though odd in meaning)
• Burası kalabalık. = This place is crowded.
• Burası kalabalıktı. = This place was crowded.

So the plain form kalabalık is exactly what you expect here.

A rough English-friendly pronunciation is:

• Vagon ≈ vah-GON
• çok ≈ chok
• kalabalık ≈ kah-lah-bah-LUK

A few notes:

• ç is pronounced like ch in chair
• o is a clear o sound, not a diphthong
• ı is the Turkish sound with no exact English equivalent; it is like a short, dull uh / i sound made without rounding your lips

So the whole sentence is roughly:

• vah-GON chok kah-lah-bah-LUK

Yes.

• Vagon kalabalık. = The carriage is crowded.
• Vagon çok kalabalık. = The carriage is very crowded.

Adding çok just makes the meaning stronger.

Yes, it is completely natural.

A Turkish speaker could easily say this in situations like:

• on a train platform
• while getting on a train
• while texting someone about the trip

It sounds simple and normal. Depending on context, people might also say things like:

• Tren çok kalabalık. = The train is very crowded.
• Bu vagon çok kalabalık. = This carriage is very crowded.
• İçerisi çok kalabalık. = It’s very crowded inside.

But your sentence itself is perfectly natural.