Når filmen er slut, går vi hjem.

Here når means when in the sense of a general or future situation:

• Når filmen er slut, går vi hjem. = when the film is over, we go home / we’ll go home.

A useful contrast is:

• når = when for something that happens in the future or happens regularly
• da = when for a specific event in the past

Examples:

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

So in your sentence, når is the natural choice.

Danish often uses the present tense for future meaning when the time is already clear from the context.

Because når filmen er slut clearly points to a later time, Danish does not need a special future form here.

So:

• Når filmen er slut, går vi hjem.

naturally means something like:

• When the film is over, we’ll go home.

This is very common in Danish. You do not need vil here.

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

The sentence starts with the subordinate clause:

• Når filmen er slut

After that, the main clause begins, and the finite verb must come first in that main clause:

• går vi hjem

So the structure is:

• subordinate clause
• finite verb
• subject
• rest of sentence

That is why you get:

• Når filmen er slut, går vi hjem.

and not:

• Når filmen er slut, vi går hjem.

In Danish, the definite article is usually attached to the noun as an ending.

So:

• en film = a film
• filmen = the film

This is one of the big differences from English. Instead of a separate word like the, Danish often adds:

• -en for many common-gender nouns
• -et for many neuter nouns

Here film is a common-gender noun, so:

• film
  • -en = filmen

Er slut means is over or is finished.

In this sentence, it describes the state of the film once it has ended. It is a very natural way to say that something like a film, concert, lesson, or meeting is over.

Examples:

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

A related sentence would be:

• Når filmen slutter, går vi hjem.

That means when the film ends.
The difference is small:

• er slut focuses on the state: is over
• slutter focuses on the event: ends

Both can work, but er slut is very idiomatic here.

No. They are completely unrelated in meaning.

In Danish, slut is a normal everyday word meaning:

• finished
• over
• the end

So in filmen er slut, there is nothing rude or strange at all. It is a completely neutral word.

This is the classic Danish distinction between movement and location:

• hjem = homeward, to home
• hjemme = at home

Because går vi hjem involves movement, Danish uses hjem.

Compare:

• Vi går hjem. = We go home.
• Vi er hjemme. = We are at home.

So:

• gå hjem = go home
• være hjemme = be at home

Because hjem already works as an adverb meaning home/homeward.

So Danish normally says:

• gå hjem
• komme hjem
• køre hjem

not gå til hjem.

This is similar to English, where we also say go home, not go to home.

Because Når filmen er slut is a subordinate clause, and it is separated from the main clause by a comma.

So the sentence divides like this:

• Når filmen er slut, = subordinate clause
• går vi hjem. = main clause

The comma helps show where the subordinate clause ends and where the main clause begins.

Yes, you can.

• Når filmen er slut, går vi hjem.
• Når filmen er slut, så går vi hjem.

Both are possible.

The version without så is very standard and neutral.
Adding så can make the sentence sound a bit more spoken, a bit more pointed, or a bit more flowing in conversation.

So as a learner, the safest default is:

• Når filmen er slut, går vi hjem.

But if you hear så in speech, that is normal too.