Wir sitzen im letzten Waggon, weil es in diesem Abteil ruhiger ist.

Because this sentence describes location, not movement.

• in + dative = being in a place
• in + accusative = moving into a place

So:

• Wir sitzen im letzten Waggon = we are sitting in the last carriage
• Wir gehen in den letzten Waggon = we are going into the last carriage

Here, sitzen shows a fixed position, so German uses the dative.

im is just a contraction of in dem.

• in dem letzten Waggon
• contracted: im letzten Waggon

This contraction is very common in German.

A few similar ones:

• am = an dem
• vom = von dem
• zum = zu dem

Because letzten is the adjective ending required here.

The noun is:

• der Waggon (masculine)

And the phrase is in the dative singular because it follows in in a location sense:

• in dem letzten Waggon
• im letzten Waggon

After a definite article like dem, adjectives usually take the weak ending -en in the dative singular masculine and neuter.

So:

• dem letzten Waggon
• diesem Abteil

Because weil introduces a subordinate clause, and in German subordinate clauses are separated by a comma.

So the sentence is split into:

• Wir sitzen im letzten Waggon
• weil es in diesem Abteil ruhiger ist

This is standard German punctuation.

Because weil is a subordinating conjunction, and subordinating conjunctions send the conjugated verb to the end of the clause.

Main clause:

• Wir sitzen im letzten Waggon

Subordinate clause:

• weil es in diesem Abteil ruhiger ist

Compare:

• Es ist in diesem Abteil ruhiger.
• ..., weil es in diesem Abteil ruhiger ist.

That verb-final position is one of the most important patterns to learn with words like:

• weil = because
• dass = that
• wenn = if/when
• obwohl = although

Here, es is the subject of ist.

German often uses es in sentences about general conditions or situations, especially with adjectives like:

• ruhig = quiet
• kalt = cold
• angenehm = pleasant

So:

• Es ist ruhig. = It is quiet.
• Es ist hier kalt. = It is cold here.

In your sentence:

• weil es in diesem Abteil ruhiger ist = because it is quieter in this compartment

The es does not refer to a specific thing like the compartment. It is more like the English it in it is quiet.

Because Abteil is a neuter noun:

• das Abteil = the compartment

And after in with a location meaning, you need the dative:

• in diesem Abteil

The article word diesem is the dative singular form of dieses.

Compare:

• dieses Abteil = this compartment (nominative/accusative)
• in diesem Abteil = in this compartment (dative)

ruhiger is the comparative form of ruhig.

• ruhig = quiet
• ruhiger = quieter

The sentence means that this compartment is quieter than some other place, even though German does not explicitly say what it is being compared with.

That comparison is understood from the context, for example:

• quieter than the other compartments
• quieter than the rest of the train
• quieter than the front car

German often uses the comparative without stating than ... if the comparison is obvious.

Yes. If you want to state the comparison explicitly, you can add als:

• ..., weil es in diesem Abteil ruhiger ist.
• ..., weil es in diesem Abteil ruhiger ist als vorne.
• ..., weil es hier ruhiger ist als in den anderen Waggons.

Without als, the sentence still sounds completely natural if the comparison is clear from context.

Because sitzen is more specific.

• sein = to be
• sitzen = to be sitting

So:

• Wir sind im letzten Waggon. = We are in the last carriage.
• Wir sitzen im letzten Waggon. = We are sitting in the last carriage.

The version with sitzen gives more detail about what the people are doing.

No, Waggon is not the only possibility.

Common related words include:

• der Waggon = carriage / rail car
• der Wagen = car, carriage, coach; also used for train cars in some contexts

In everyday modern German, many speakers might also say things like:

• im letzten Wagen

But Waggon is perfectly understandable and specifically train-related in this context.

In standard German, weil normally takes verb-final word order:

• ..., weil es in diesem Abteil ruhiger ist.

In informal spoken German, you may sometimes hear:

• ..., weil es ist hier ruhiger.

But that is colloquial and not the standard form learners should copy. For correct written German and careful speech, use verb-final after weil.