Auf nasser Fahrbahn fährt sie langsamer, damit sie besser bremsen kann.

No. Auf nasser Fahrbahn is not the subject; it is a prepositional phrase meaning something like on wet road surface / on a wet roadway.

The subject is sie.

German often puts a time, place, or condition phrase first for emphasis. Even when something other than the subject comes first, the conjugated verb still stays in second position:

• Auf nasser Fahrbahn | fährt | sie langsamer

That is standard German verb-second word order in a main clause.

Because German main clauses usually follow the verb-second rule.

If the subject comes first, you get:

• Sie fährt langsamer.

But if another element is moved to the front, the verb still has to stay second, so the subject moves after it:

• Auf nasser Fahrbahn fährt sie langsamer.

This is very common in German and can feel unusual to English speakers, because English does not move the subject this way.

Because auf can take either the accusative or the dative, depending on meaning.

• accusative: movement onto something
• dative: location or situation on something

Here, the sentence describes the situation on a wet road surface, not movement onto it, so German uses the dative:

• auf nasser Fahrbahn

Since Fahrbahn is feminine, and there is no article, the adjective takes the strong dative feminine ending -er:

• nasser Fahrbahn

German often omits the article in general statements, especially in phrases like this.

So auf nasser Fahrbahn means something like:

• on wet road surfaces
• when the road is wet
• on a wet roadway

It sounds general, not tied to one specific road.

If you wanted to refer to a specific wet road surface, you could say:

• auf der nassen Fahrbahn

That would mean on the wet road surface.

Not exactly.

• Straße = street/road in a general sense
• Fahrbahn = the part of the road used by vehicles, roughly carriageway / roadway / traffic lane area

In everyday English, learners may simply translate it as road, but Fahrbahn is a bit more technical and specific.

Because langsamer is the comparative form, meaning more slowly.

• langsam = slow / slowly
• langsamer = slower / more slowly

Here it describes how she drives, so in English we would usually say:

• She drives more slowly

In German, adjectives and adverbs usually have the same form, so langsamer can mean either slower or more slowly, depending on context.

Yes, the infinitive is fahren. But fahren is a strong verb, and in the 2nd and 3rd person singular present tense, the stem vowel often changes from a to ä.

So:

• ich fahre
• du fährst
• er/sie/es fährt
• wir fahren
• ihr fahrt
• sie/Sie fahren

That is why the sentence has sie fährt.

Here damit means so that and introduces a purpose clause.

So:

• ..., damit sie besser bremsen kann.
• ..., so that she can brake better.

It explains the purpose of driving more slowly.

Because damit introduces a subordinate clause, and in German subordinate clauses are separated from the main clause with a comma.

So the structure is:

• Main clause: Auf nasser Fahrbahn fährt sie langsamer
• Subordinate clause: damit sie besser bremsen kann

The comma is required.

Because damit introduces a subordinate clause, and in German subordinate clauses send the conjugated verb to the end.

Compare:

• Main clause: Sie kann besser bremsen.
• Subordinate clause: ..., damit sie besser bremsen kann.

That final-verb pattern is one of the most important features of German subordinate clauses.

Because kann is a modal verb, and with a modal verb German uses:

• infinitive + modal verb at the end of the subordinate clause

So:

• besser bremsen kann

In a main clause, you would see:

• Sie kann besser bremsen.

But in the subordinate clause after damit, the finite modal moves to the end:

• ..., damit sie besser bremsen kann.

Yes, it could.

Because the subject is the same in both parts of the sentence, German could also say:

• Auf nasser Fahrbahn fährt sie langsamer, um besser bremsen zu können.

That also means She drives more slowly on wet roads in order to be able to brake better.

A useful rule is:

• um ... zu is common when the subject is the same
• damit is necessary when the subject is different

In this sentence, both are possible, though damit makes the purpose especially explicit.

Here it means she, because the verb is singular:

• sie fährt = she drives

If it meant they, the verb would be plural:

• sie fahren = they drive

So the verb form tells you which meaning is intended.