Hvis vejen er glat, kører jeg langsomt, så jeg kommer sikkert hjem.

Hvis means a condition: if. It is used when something may or may not be true.

Når usually means when, and it is more natural when you are talking about something that actually happens or is expected to happen. So:

• Hvis vejen er glat = if the road is slippery
• Når vejen er glat = when the road is slippery

In this sentence, hvis is the right choice because it presents a condition.

Vej means road.
Vejen means the road.

In Danish, the definite article is usually added to the end of the noun instead of being a separate word in front, so:

• en vej = a road
• vejen = the road

That is a very common pattern in Danish.

Because vejen is singular, and the adjective is in the singular form.

Here glat is the correct form after er:

• Vejen er glat = The road is slippery
• Vejene er glatte = The roads are slippery

So glatte would be used for plural, not for singular vejen.

Danish often uses the present tense for general situations, habits, and even some future-like meanings, just as English can.

This sentence describes a general rule or typical behavior: whenever that condition is true, this is what happens. So the present tense sounds natural.

Compare:

• Hvis vejen er glat, kører jeg langsomt = a general statement
• It does not have to mean only right now

This is because of the Danish verb-second rule in main clauses.

The first part, Hvis vejen er glat, is a subordinate clause placed at the beginning. After that, the main clause must still have the finite verb in the second position, so Danish uses inversion:

• Hvis vejen er glat, kører jeg langsomt

Not:

• Hvis vejen er glat, jeg kører langsomt

This is a very important word-order pattern in Danish.

Because langsomt is being used as an adverb, modifying the verb kører.

The adjective is langsom = slow.
When Danish often turns this kind of adjective into an adverb, it uses the -t form:

• en langsom bil = a slow car
• Han er langsom = He is slow
• Han kører langsomt = He drives slowly

So here langsomt means slowly.

Here så means something like so or so that. It links the action driving slowly with the result or purpose getting home safely.

So it is not the time-sequence then meaning here. It is more about consequence or intention:

• ..., så jeg kommer sikkert hjem
  = ..., so that / so I get home safely

Here sikkert means safely, not probably.

That matters because Danish sikkert can mean two different things:

• safely = adverb of manner
• probably = sentence adverb

In this sentence, it comes after the verb because it describes how I get home:

• kommer sikkert hjem = get home safely

If sikkert meant probably, the word order would often be different, especially in more formal grammar patterns. So the position here helps show that the meaning is safely.

Because hjem is a very common adverb meaning homeward / home.

Danish often uses hjem without a preposition when someone is going or coming home:

• jeg går hjem = I walk home
• jeg kommer hjem = I get home / come home

By contrast:

• hjemme means at home
• hjem means movement to home

So kommer sikkert hjem is completely natural.

The commas separate the different clauses.

• Hvis vejen er glat = subordinate clause
• kører jeg langsomt = main clause
• så jeg kommer sikkert hjem = following clause expressing result or purpose

So the commas help show the structure clearly. Danish comma usage is not always identical to English comma usage, but these commas are normal and useful in this sentence.