Wir rauchen nicht im Auto.

Wir means we. It is the subject of the sentence—the people doing the action.

So in Wir rauchen nicht im Auto, wir tells you who is involved: we.

Because the subject is wir (we), the verb has to match that subject.

The verb is rauchen = to smoke.

Its present-tense forms are:

• ich rauche = I smoke
• du rauchst = you smoke
• er/sie/es raucht = he/she/it smokes
• wir rauchen = we smoke
• ihr raucht = you all smoke
• sie/Sie rauchen = they/you (formal) smoke

So with wir, the correct form is rauchen.

In a normal German main clause, the conjugated verb usually comes in position 2. This is often called the V2 rule.

Here the sentence is:

• Wir = position 1
• rauchen = position 2
• nicht im Auto = the rest

So Wir rauchen nicht im Auto follows standard German word order.

Nicht usually goes before the part of the sentence it is negating, or near the end if it negates the whole statement.

Here, nicht im Auto means not in the car / we do not smoke in the car.

So the sentence structure shows that the smoking is being negated in that setting.

This placement is natural and standard:

• Wir rauchen nicht im Auto.

If you moved nicht, the emphasis could change, and some versions would sound less natural.

Because nicht negates verbs, adjectives, whole clauses, or specific parts of a sentence.
Kein is mainly used to negate a noun that would otherwise have ein or no article.

Here, you are negating the action rauchen (to smoke), so you use nicht:

• Wir rauchen nicht im Auto. = We do not smoke in the car.

Compare:

• Wir rauchen keine Zigaretten im Auto. = We smoke no cigarettes / We do not smoke cigarettes in the car.

There, keine negates the noun Zigaretten.

Im is a contraction of in dem.

• in = in
• dem = the (dative masculine/neuter)

So:

• im Auto = in the car

German often combines certain prepositions and articles like this:

• im = in dem
• am = an dem
• zum = zu dem

Because German uses different cases after in depending on meaning.

In can take:

• dative for location: in the car
• accusative for movement into something: into the car

Here, the meaning is location: the smoking happens inside the car, not movement into the car.

So German uses the dative:

• in dem Auto → im Auto

If it were movement, you would get accusative:

• Wir gehen in das Auto. = We go into the car.
  (Though in real German, ins Auto is more common: in das → ins.)

Because Auto is a noun, and all nouns are capitalized in German.

So:

• Auto = noun → capitalized
• rauchen = verb → not capitalized
• nicht = adverb → not capitalized

This is one of the most noticeable spelling rules in German.

Yes, Auto is a neuter noun:

• das Auto = the car

That is why after in with dative you get:

• dem Auto

and with the contraction:

• im Auto

Yes. That is also correct German.

German still keeps the verb in second position, but you can move another element to the front for emphasis:

• Wir rauchen nicht im Auto. = neutral
• Im Auto rauchen wir nicht. = emphasizes in the car

This second version sounds like: In the car, we don’t smoke.

So the meaning is basically the same, but the focus changes.

It is possible in some contexts, but it is not the most neutral or natural version here.

Wir rauchen nicht im Auto is the standard sentence.

Putting nicht at the very end often changes the emphasis and can sound marked, as if you are correcting someone or contrasting with something else.

So for a learner, the safest and most natural version is:

• Wir rauchen nicht im Auto.

No. Rauchen can be used without naming what is being smoked.

So:

• Wir rauchen. = We smoke.

That is already complete.

If you want, you can add an object:

• Wir rauchen Zigaretten. = We smoke cigarettes.

But in your sentence, German does not need an object.

English often uses do for negation:

• We do not smoke in the car.

German does not do that here. It simply uses the normal verb plus nicht:

• Wir rauchen nicht im Auto.

So German does not need an extra helper word like English do in this kind of sentence.

A rough pronunciation is:

• rauchen ≈ ROW-khen

A few details:

• au sounds like the ow in cow
• ch in rauchen is the softer German ch sound, not an English k or ch as in chair
• -en is a light ending, often not strongly pronounced

And the full sentence is roughly:

• Wir rauchen nicht im Auto
  ≈ Veer ROW-khen nikht im OW-toh

That is only an approximation, but it can help as a starting point.