Du ska stänga dörren när du går ut.

Because ska is a modal verb here. After a modal verb in Swedish, the main verb stays in the infinitive form.

• du ska stänga = you should / must / are to close
• du stänger = you close / you are closing

So stänga is used because it follows ska.

In this sentence, ska gives a sense of instruction, expectation, or obligation.

Depending on context, du ska can mean things like:

• you should
• you must
• you are supposed to
• you will sometimes, but not usually here

In Du ska stänga dörren när du går ut, it sounds like an instruction: You should / must close the door when you go out.

Because Swedish uses the definite form here: dörren = the door.

• en dörr = a door
• dörren = the door

The definite article is usually added as an ending in Swedish, instead of using a separate word like the in English.

Because this part is a normal finite clause: du går ut = you go out.

Here, går is the present tense of gå.

• gå = infinitive, to go
• går = present tense, go / are going

So:

• du ska stänga → modal + infinitive
• du går ut → normal clause with a present-tense verb

Ut means out.

With gå, it forms gå ut, which means go out.

Examples:

• gå ut = go out
• komma ut = come out
• ta ut = take out

In this sentence, du går ut means you go out / you leave.

Because när is used when something is expected to happen, not just hypothetical.

• när = when
• om = if

So:

• när du går ut = when you go out
  (you are expected to go out at some point)

• om du går ut = if you go out
  (maybe you will, maybe you will not)

In your sentence, när is the natural choice because it assumes the action will happen.

Yes, it can.

Du ska + infinitive is often used to give instructions, especially in speech. It can sound:

• firm
• parental
• authoritative
• like a rule

For example:

• Du ska stänga dörren. = You should/must close the door.

A more direct imperative would be:

• Stäng dörren! = Close the door!

So du ska stänga dörren is less like a blunt command and more like This is what you are supposed to do.

Because när du går ut is a subordinate clause, and Swedish keeps the subject before the verb there.

So:

• du går ut = subject + verb + particle
• när du går ut = when you go out

This is normal Swedish subordinate clause word order.

A useful comparison:

• Main clause: Du stänger dörren.
• Subordinate clause: ... när du går ut.

The order still stays natural here: du går.

Yes, but it changes the meaning slightly.

• när du går ut = when you go out
• innan du går ut = before you go out

So:

• Du ska stänga dörren när du går ut.
  = close the door when leaving

• Du ska stänga dörren innan du går ut.
  = close the door before you go out

Both are possible, but innan emphasizes the action happening first.

It refers to a future or repeated situation, even though Swedish often uses present forms in these cases.

• ska stänga points to something that is expected or required
• när du går ut uses present tense, but means when you go out in the future or whenever that happens

This is very common in Swedish. English often does something similar:

• Close the door when you go out.

Even though go is present tense, the meaning refers to a future occasion.

A rough guide is STENG-a, but the vowel is not exactly like English.

A few points:

• ä sounds somewhat like the vowel in English bed, though not identical
• ng in stänga sounds like the ng in sing
• the g after ng is usually heard as a separate consonant here

So stänga is approximately STENG-ga.

Also:

• dörren has an ö sound that English does not really have
• går has an å sound, something like a broad o

If you want, I can also break the whole sentence down word by word with pronunciation help.

In modern Swedish, du is normally singular: you when speaking to one person.

For more than one person, Swedish often uses:

• ni = you (plural)

So if you were telling several people, you would normally say:

• Ni ska stänga dörren när ni går ut.

That said, many learner translations just use English you, since English does not usually distinguish singular and plural in modern everyday language.