Der Fahrer darf den Hund nicht überfahren.

Because in German, all nouns are capitalized.

So in this sentence:

• der Fahrer = the driver
• der Hund = the dog

This is one of the first big spelling differences English speakers notice.

Der Fahrer is the subject of the sentence — the one doing the action or being talked about.

German marks that role with case. Here, the subject is in the nominative case.

• der = masculine nominative singular
• Fahrer = driver

So der Fahrer means the driver as the subject.

Because den Hund is the direct object — the thing affected by the action.

The verb überfahren takes a direct object, and a masculine noun in the accusative case uses den, not der.

So:

• der Hund = the dog as a subject
• den Hund = the dog as a direct object

That is why the sentence has den Hund.

Darf is the 3rd person singular present tense of dürfen, a modal verb.

Its basic meaning is:

• dürfen = to be allowed to / may

So:

• er darf = he is allowed to / he may

But in the negative, nicht dürfen usually means:

• must not
• is not allowed to

So in this sentence, it is not just weak possibility. It expresses prohibition.

Because after a modal verb like dürfen, the main verb usually stays in the infinitive.

So German does this:

• Der Fahrer darf ... überfahren.

not:

• Der Fahrer darf ... überfährt.

The conjugated verb is darf, and überfahren stays in its basic form.

That is normal German word order with a modal verb in a main clause.

German often works like this:

• the conjugated verb goes in position 2
• the infinitive goes to the end

So the structure is:

• Der Fahrer = subject
• darf = conjugated modal verb
• den Hund nicht überfahren = the rest, with the infinitive at the end

English speakers often find this strange at first, but it is very common in German.

Here, nicht is negating the action überfahren.

A very common pattern with modal verbs is:

• modal verb + object + nicht + infinitive

So:

• Der Fahrer darf den Hund nicht überfahren.

This means the action of running over the dog is not allowed.

In neutral word order, this placement sounds natural.

In most normal situations, nicht dürfen means must not / is not allowed to.

That is important, because English may not can be ambiguous:

• You may not go can mean you are not allowed to go
• but it can also sound like perhaps you won’t go

German nicht dürfen is usually not ambiguous in that way. It normally expresses a rule or prohibition.

So this sentence is best understood as:

• The driver must not run over the dog
• The driver is not allowed to run over the dog

No — in this sentence, überfahren is the inseparable verb meaning to run over.

That matters because some German verbs with prefixes can be separable or inseparable depending on meaning.

Here, the clue is what happens when the verb is used without a modal:

• Der Fahrer überfährt den Hund nicht.

You do not say:

• Der Fahrer fährt den Hund nicht über.

So for this meaning, it behaves as an inseparable verb.

In this meaning, the stress is on fahren, not on über:

• überFAHren

That stress pattern goes with the inseparable verb meaning to run over.

A learner does not need perfect phonetics immediately, but it helps to know that the stress is not on the first syllable here.

Yes, but changing the word order usually changes the focus or emphasis.

The most neutral version is:

• Der Fahrer darf den Hund nicht überfahren.

If you say:

• Der Fahrer darf nicht den Hund überfahren.

that sounds more like:

• It is not the dog that the driver may run over
  or
• The driver must not run over the dog specifically

In other words, it sounds contrastive, as if you are correcting someone.

So the original sentence is the normal, neutral way to say it.

Grammatically, der Fahrer is a masculine noun.

In many contexts, that suggests a male driver. A specifically female form would be:

• die Fahrerin

However, depending on context, masculine job nouns have sometimes also been used more generally. Still, in a simple sentence like this, many learners should understand der Fahrer as most naturally referring to a male driver.