Lyset i gangen slukkes, når alle går i seng.

Because Danish usually puts the definite article at the end of the noun.

• lys = light
• lyset = the light
• gang = hallway/corridor
• gangen = the hallway

So lyset i gangen is literally something like light-the in hallway-the, but natural English is the light in the hallway.

The endings also show gender:

• common gender nouns often take -en in the definite singular
• neuter nouns often take -et

So:

• gang is common gender → gangen
• lys is neuter → lyset

Slukkes is the passive form of slukke, which means to switch off, to turn off, or to extinguish.

So lyset slukkes means:

• the light is turned off
• or the light gets turned off

The sentence does not say who does it. It focuses on what happens to the light.

Because slukker is active, while slukkes is passive.

• slukker = turns off / switches off
• slukkes = is turned off

Compare:

• Han slukker lyset = He turns off the light.
• Lyset slukkes = The light is turned off.

In your sentence, the light is receiving the action, so the passive fits.

Yes. Slukkes is present tense passive.

Danish, like English, often uses the present tense for things that happen regularly or as a general rule. This sentence describes a routine or normal situation, not one single event.

So it has the sense of:

• The light in the hallway is turned off when everyone goes to bed.

It is not necessarily happening right now; it is just what normally happens.

Because når is the normal word for when in repeated, general, or future situations.

Here is the difference:

• når = when / whenever
• da = when, but usually about a specific past event
• hvis = if

So in this sentence, når works because it means something like whenever everyone goes to bed.

Examples:

• Når alle går i seng, slukkes lyset. = Whenever everyone goes to bed, the light is turned off.
• Da alle gik i seng, blev lyset slukket. = When everyone went to bed, the light was turned off.
  
  • This refers to a specific past situation.
• Hvis alle går i seng, slukkes lyset. = If everyone goes to bed, the light is turned off.
  
  • This sounds conditional instead of simply stating the usual sequence.

Because når alle går i seng is a subordinate clause, and Danish subordinate clauses normally keep the basic subject + verb order.

So:

• når alle går i seng = when everyone goes to bed

not:

• når går alle i seng

Inversion like går alle is typical in main clauses after certain elements, but not here.

Then the main clause changes word order.

You can say:

• Når alle går i seng, slukkes lyset i gangen.

This is also correct.

Why does it become slukkes lyset instead of lyset slukkes?
Because in Danish main clauses, when something else comes first, the finite verb usually takes second position.

So:

• Lyset i gangen slukkes, når alle går i seng.
• Når alle går i seng, slukkes lyset i gangen.

Both are correct; the difference is mainly emphasis and sentence flow.

Yes, gå i seng is a very common fixed expression meaning to go to bed.

Word by word:

• går = goes / is going
• i = in / into
• seng = bed

But as a whole, gå i seng simply means go to bed.

This is one of those expressions where Danish does not match English word-for-word. You should learn it as a chunk.

Because gå i seng is an idiomatic expression, and in this expression Danish uses the noun without the definite article.

So:

• gå i seng = go to bed

This does not usually mean walking into a specific physical bed. It means going to bed as an activity or routine.

If you say i sengen, that sounds more like in the bed or in the specific bed.

Compare:

• Børnene går i seng klokken otte. = The children go to bed at eight.
• Børnene leger i sengen. = The children are playing in the bed.

Because når alle går i seng is a subordinate clause.

In Danish, many writers put a comma before a subordinate clause, as in your sentence. However, Danish comma practice has allowed more than one standard system, so you may also see the sentence written without that comma:

• Lyset i gangen slukkes når alle går i seng.

Both can be encountered, depending on the comma style being used. So the comma here is normal, but you should not be surprised if you sometimes see it omitted.

Yes, you could say:

• Lyset i gangen bliver slukket, når alle går i seng.

That also means the light in the hallway is turned off when everyone goes to bed.

The difference is mostly style and nuance:

• slukkes = shorter, more compact, often very natural in rules, statements, and general descriptions
• bliver slukket = a fuller passive, sometimes a bit more explicit or conversational

In this sentence, slukkes sounds very natural.