Nach dem Unfall ist die Fahrerin verletzt, aber sie bleibt ruhig.

Because nach is a preposition that takes the dative case in this meaning.

• der Unfall = the accident
• dative masculine/neuter article = dem
• so: nach dem Unfall = after the accident

A native English speaker often wants to say something like nach der Unfall, but that is wrong because Unfall is masculine: der Unfall.

In German, all nouns are capitalized.

So in this sentence:

• Unfall = noun
• Fahrerin = noun

Both must begin with a capital letter.

Nach dem Unfall means after the accident.

It is a time expression placed at the beginning of the sentence. German often puts time phrases first for emphasis or simply for style.

So this sentence is literally structured like:

• After the accident, the driver is injured, but she remains calm.

Putting that phrase first affects word order in the first clause.

Because when German puts something in the first position of a main clause, the finite verb must still come in second position. This is the verb-second rule.

So:

• normal order: Die Fahrerin ist verletzt.
• with a phrase moved to the front: Nach dem Unfall ist die Fahrerin verletzt.

The first position is taken by Nach dem Unfall, so the verb ist must come next.

Yes. Die Fahrerin means the female driver.

German often distinguishes male and female forms:

• der Fahrer = male driver / driver in a masculine form
• die Fahrerin = female driver

The ending -in is a very common way to form feminine nouns referring to people.

Yes. Sie here means she, and it refers back to die Fahrerin.

Since Fahrerin is singular and female, the pronoun is:

• sie = she

Be careful: sie can also mean:

• they
• you (formal, when capitalized as Sie)

But here, from the context, it clearly means she.

In German, verletzt is usually used as an adjective or as a past participle functioning adjectivally in this kind of sentence.

So:

• Sie ist verletzt. = She is injured.

This is very natural German. It works like an adjective describing her condition.

You can think of it as similar to English She is hurt/injured.

Both are possible, but they mean slightly different things.

• ist ruhig = is calm
  This describes her state.
• bleibt ruhig = remains calm / stays calm
  This emphasizes that she continues to be calm despite the situation.

In this sentence, bleibt ruhig is a good choice because it contrasts with the accident and injury: even so, she stays calm.

Because ruhig is used here as a predicate adjective, after the verb bleibt. Predicate adjectives in German do not take adjective endings.

Compare:

• die ruhige Fahrerin = the calm driver
  Here the adjective comes before the noun, so it takes an ending: ruhige
• Die Fahrerin bleibt ruhig.
  Here it comes after the verb, so there is no ending

The same is true with verletzt:

• die verletzte Fahrerin = the injured driver
• Die Fahrerin ist verletzt.

Aber means but and connects two main clauses:

1. Nach dem Unfall ist die Fahrerin verletzt
2. sie bleibt ruhig

It shows contrast:

• she is injured, but
• she remains calm

After aber, German does not force the verb to the end. The second part is still a normal main clause, so sie bleibt ruhig keeps normal main-clause word order.

Yes, that is grammatically correct, but the focus changes.

Original sentence:

• first says she is injured
• then contrasts that with the fact that she stays calm

Your version:

• first emphasizes that she remains calm
• then adds that she is injured

So both are correct, but they present the information differently.

Not always. Nach can mean different things depending on context, for example:

• after in time: nach dem Unfall = after the accident
• to with cities/countries without an article: nach Berlin
• according to: nach dem Bericht

So in this sentence, it specifically means after.

Then you would use the masculine noun and pronoun:

• Nach dem Unfall ist der Fahrer verletzt, aber er bleibt ruhig.

Changes:

• die Fahrerin → der Fahrer
• sie → er

Everything else stays the same.

Yes. In this sentence, both function as predicate adjectives:

• ist verletzt = describes her condition
• bleibt ruhig = describes her state

So even though verletzt originally comes from a verb (verletzen = to injure), here it behaves like an adjective in the sentence.

A rough word-for-word breakdown is:

• Nach dem Unfall = After the accident
• ist = is
• die Fahrerin = the female driver
• verletzt = injured
• aber = but
• sie = she
• bleibt = remains/stays
• ruhig = calm

So the full structure is:

After the accident, is the female driver injured, but she remains calm.

That sounds odd in English because English word order is different, but it helps show the German structure.