Da kampen var slut, købte vi is, og bagefter gik vi langs havnen, mens solen langsomt forsvandt.

Here da means when, but specifically for a single event in the past.

• Da kampen var slut = When the match was over
• It points to one particular moment.

A very common contrast is:

• da = when for a specific past event
• når = when for repeated situations, general truths, or future meaning

Examples:

• Da jeg kom hjem, spiste vi. = When I got home, we ate.
• Når jeg kommer hjem, spiser vi. = When I get home, we eat / will eat.

So da is the right choice here because the sentence describes one finished event in the past.

This is because Danish main clauses follow the V2 rule: the finite verb normally comes in the second position.

In this sentence, the first position is already taken by the whole time clause:

• Da kampen var slut

So the next element must be the finite verb:

• købte

And then comes the subject:

• vi

So the structure is:

• Da kampen var slut, købte vi is.

Not:

• Da kampen var slut, vi købte is.

This verb-second pattern is one of the most important parts of Danish word order.

Because slut here is an adjective, meaning over or finished.

• Kampen var slut = The match was over.

By contrast, sluttet is the past participle of slutte and is used in other structures, such as perfect tenses or passive-like meanings.

Compare:

• Filmen er slut. = The film is over.
• Mødet er sluttet. = The meeting has ended.

In everyday Danish, være slut is the natural way to say that something is over.

In Danish, food and drink are often used without an article when you mean the substance or activity in a general way.

So:

• købe is = buy ice cream
• spise is = eat ice cream
• drikke kaffe = drink coffee

This is similar to English in some cases, but Danish often does it where English might also say an ice cream.

If you want to emphasize one specific item or portion, you can use an article:

• Vi købte en is. = We bought an ice cream.

So both are possible, but købte vi is sounds natural if the focus is just on the activity or treat, not on counting individual items.

Bagefter means afterwards, after that, or later.

It is placed first to show the sequence of events clearly:

• first they bought ice cream
• bagefter they walked along the harbor

Because bagefter is in first position in a main clause, Danish again uses the V2 rule:

• og bagefter gik vi langs havnen

not

• og bagefter vi gik langs havnen

So fronting bagefter changes the word order in the same way as the opening da-clause did.

Again, this is the V2 rule.

Even though the clause starts with og, the important first element after that is bagefter. Since bagefter comes first, the finite verb must come next:

• og bagefter gik vi ...

Think of it like this:

• first position: bagefter
• second position: gik
• then subject: vi

So Danish says:

• Og bagefter gik vi langs havnen

where English would keep normal subject-verb order:

• And afterwards we walked along the harbor

Langs is a preposition meaning along.

So:

• langs havnen = along the harbor

A few useful points:

• langs is followed directly by the noun
• the noun stays in its normal form; Danish does not change noun endings for case the way some languages do
• havnen is the definite form, meaning the harbor

Why definite?

Because it sounds like a specific harbor known from the situation or setting. Danish often uses the definite form when the place is understood from context.

Compare:

• langs havnen = along the harbor
• langs en havn = along a harbor

The first is much more natural here.

Mens means while.

It introduces a subordinate clause that describes what was happening at the same time as the main action:

• gik vi langs havnen = we walked along the harbor
• mens solen langsomt forsvandt = while the sun slowly disappeared

So mens connects two actions happening simultaneously.

It is a very common subordinating conjunction, like da, når, fordi, and hvis.

Because mens introduces a subordinate clause, and subordinate clauses do not use the same V2 inversion as main clauses.

So the normal order is:

• mens + subject + verb

Here:

• mens solen ... forsvandt

That is why you get:

• mens solen langsomt forsvandt

not

• mens forsvandt solen ...

This is an important contrast:

• main clause: often V2
  
  • Bagefter gik vi ...
• subordinate clause: subject before finite verb
  
  • mens solen ... forsvandt

Yes. The whole sentence tells a past narrative, so all the finite verbs are in the past tense:

• var = past of være (to be)
• købte = past of købe (to buy)
• gik = past of gå (to walk/go)
• forsvandt = past of forsvinde (to disappear)

A useful thing to notice is that some are regular and some are irregular:

• købe → købte = regular
• gå → gik = irregular
• forsvinde → forsvandt = irregular
• være → var = irregular

So this sentence is a nice example of Danish past-tense storytelling.

The commas mark the different clause boundaries.

1. Da kampen var slut,
   The opening subordinate clause is followed by a comma.

2. købte vi is, og bagefter gik vi langs havnen
   There is a comma before og because it links two full main clauses.

3. langs havnen, mens solen langsomt forsvandt
   The comma before mens marks the start of a subordinate clause.

One small note: Danish comma usage can vary a little depending on the comma system being used, especially before subordinate clauses, but the punctuation in your example is completely standard and helpful for showing the structure clearly.