Im letzten Waggon war noch ein Platz frei, also haben wir uns dort hingesetzt.

Because this phrase describes a location: the free seat was in the last carriage.

With in, German uses:

• dative for a static location: in dem/ im Waggon
• accusative for movement into something: in den Waggon

So here:

• Im letzten Waggon war noch ein Platz frei = In the last carriage, there was still a seat free

If it were about moving into the carriage, you would use accusative:

• Wir gingen in den letzten Waggon.

im is a contraction of in dem.

So:

• im letzten Waggon = in dem letzten Waggon

This contraction is extremely common in German.

Other common ones are:

• am = an dem
• zum = zu dem
• zur = zu der

Because letzten is an adjective describing Waggon, and adjective endings depend on:

• the case
• the gender
• the article

Here, Waggon is masculine: der Waggon.
After im = in dem, it is dative masculine singular.

In that combination, the adjective takes -en:

• in dem letzten Waggon

So letzten is just the correct adjective ending for dative masculine after a definite article.

Because ein Platz is the subject of the clause, so it is in the nominative case.

The structure is:

• Ein Platz war frei.
• A seat was free / available.

Since Platz is masculine, the nominative form with the indefinite article is:

• ein Platz

You would use einen Platz only in the accusative, for example:

• Wir suchen einen Platz.
• We are looking for a seat.

Here noch means something like still or yet.

So:

• noch ein Platz frei means there was still a free seat left

It suggests that availability remained at that point.

Compare:

• Es war ein Platz frei. = There was a free seat.
• Es war noch ein Platz frei. = There was still a free seat.

In context, noch often adds the idea of remaining availability.

German often uses sein + frei to describe availability:

• Ein Platz war frei. = A seat was free / available.

You could also hear:

• Es gab noch einen freien Platz.
• There was still a free seat.

Both are natural, but they are built differently:

• Ein Platz war frei focuses on the seat’s state
• Es gab einen freien Platz uses an existential structure like there was

So the sentence is very idiomatic as written.

Because also is in the first position of the main clause, and German main clauses follow the verb-second rule.

That means the finite verb must come in position 2.

So:

• Also = position 1
• haben = position 2
• wir comes after that

Hence:

• also haben wir uns dort hingesetzt

This is the same pattern as:

• Dann gingen wir nach Hause.
• Deshalb blieb er dort.

If you started with wir, then it would be:

• Wir haben uns also dort hingesetzt.

That would change the emphasis a bit.

Yes. sich hinsetzen is a reflexive verb.

It means to sit down.

So you say:

• ich setze mich hin
• du setzt dich hin
• wir setzen uns hin

In the sentence:

• haben wir uns dort hingesetzt

uns means ourselves, though in English we usually do not translate it literally.

So the natural English meaning is just:

• we sat down there

not usually we sat ourselves down there, even though that is closer to the German structure.

These are easy to confuse:

• sitzen = to be sitting
• setzen = to set/put something, or in some contexts to seat
• sich hinsetzen = to sit down

Examples:

• Ich sitze. = I am sitting.
• Ich setze das Buch auf den Tisch. = I put the book on the table.
• Ich setze mich hin. = I sit down.

So in your sentence, hingesetzt shows the action of moving into a sitting position, not the state of already sitting.

Because the full verb is sich hinsetzen, not just sich setzen.

The particle hin- often adds the idea of movement to a place or down into position.
So:

• sich setzen can exist, but sich hinsetzen is very common for sit down
• sich dort hinsetzen = to sit down there

In the perfect tense, the separable prefix joins the participle:

• hinsetzen → hingesetzt

Compare:

• aufstehen → aufgestanden
• anmachen → angemacht

Yes, da would also be possible in many contexts.

• dort = there
• da = there

Very often, they mean nearly the same thing.
dort can sound a little more explicit or slightly more formal/written than da.

So both of these are possible:

• ... also haben wir uns dort hingesetzt.
• ... also haben wir uns da hingesetzt.

The version with dort fits well in neutral standard German.

This is the Perfekt tense:

• haben wir uns hingesetzt

In spoken German, especially in everyday conversation, Perfekt is usually preferred over Präteritum for many verbs.

So in speech, people normally say:

• Wir haben uns hingesetzt.

The simple past version would be:

• Wir setzten uns dort hin.

That is grammatical, but it sounds more literary or narrative in many contexts.

In a train context, der letzte Waggon usually means the last carriage in the train — the one at the end.

So here it most naturally refers to the carriage at the back or end of the train, not just the most recent one.

German letzte can mean last/final, and the exact nuance depends on context. In train language, it is normally understood spatially.

It is a correct word, but not the only one.

Common words include:

• der Waggon = carriage, railcar
• der Wagen = car, carriage, coach

In train contexts, many speakers also use compounds such as:

• der Zugwagen
• der Eisenbahnwagen

In everyday modern German, Wagen is often more common in some regions or contexts, but Waggon is fully understandable and standard.

Yes. German word order is flexible as long as the verb-second rule is respected.

The sentence could also be:

• Noch war im letzten Waggon ein Platz frei, also haben wir uns dort hingesetzt.
• Ein Platz war im letzten Waggon noch frei, also haben wir uns dort hingesetzt.

These versions shift the emphasis slightly.

The original:

• Im letzten Waggon war noch ein Platz frei

puts the location first, which feels very natural if the speaker is focusing on where the available seat was.