Vull que apaguis la llum quan surtis del pis.

Because the sentence has two different subjects:

• vull = I want
• apaguis = you turn off

In Catalan, when one person wants someone else to do something, you usually use:

voler + que + subjunctive

So:

• Vull apagar la llum = I want to turn off the light
• Vull que apaguis la llum = I want you to turn off the light

If the subject stays the same, Catalan often uses the infinitive. If the subject changes, que + subjunctive is very common.

After expressions of desire, will, request, or emotion, Catalan often uses the subjunctive in the subordinate clause.

Here, vull que... expresses a wish or desire, so the verb after que goes into the subjunctive:

• vull que apaguis
• not normally vull que apagues or vull que apagues la llum in standard present meaning
• not vull que apagues because that would be a different tense/form in some contexts or dialects

The present subjunctive of apagar includes:

• jo apagui
• tu apaguis
• ell/ella apaguí
• nosaltres apaguem
• vosaltres apagueu
• ells/elles apaguin

So apaguis means that you turn off / you turn off in this kind of clause.

Yes, quan means when, but in Catalan the verb after quan can also appear in the subjunctive when it refers to a future action that has not happened yet.

So:

• quan surtis del pis = when you leave the flat/apartment

This is a future situation from the speaker’s point of view: the person has not left yet.

A useful contrast:

• Quan surts del pis, tanques la porta.
  = When you leave the flat, you close the door.
  This sounds more like a habit or routine.

• Vull que apaguis la llum quan surtis del pis.
  = I want you to turn off the light when you leave the flat.
  This refers to a future action, so the subjunctive is natural.

Surtis is the 2nd person singular present subjunctive of sortir (to go out / to leave).

So here:

• quan surtis del pis = when you leave the apartment

It comes from sortir, an irregular verb. Some useful present subjunctive forms are:

• jo surti
• tu surtis
• ell/ella surti
• nosaltres sortim
• vosaltres sortiu
• ells/elles surtin

So surtis is specifically you leave in a subjunctive clause.

In this sentence, la llum is the normal way to say the light.

Catalan usually uses the definite article with concrete nouns in ordinary situations, just as English often does here:

• apagar la llum = to turn off the light
• encendre la llum = to turn on the light

You would not normally say just apagar llum. The article is needed.

Also, llum is a feminine noun, so the article is la:

• la llum

Del means of the or, in many contexts like this, it helps express from the after a verb such as sortir.

It is a contraction of:

• de + el = del

So:

• sortir del pis = to leave the flat/apartment
  literally something like to go out from the apartment

This is normal Catalan usage. After sortir, you often use de to indicate the place you are leaving:

• sortir de casa = to leave home
• sortir de l’oficina = to leave the office
• sortir del pis = to leave the apartment

Because Catalan is a pro-drop language, which means subject pronouns are often omitted when the verb ending already shows who the subject is.

Here:

• apaguis already tells you it is you
• surtis also already tells you it is you

So Catalan does not need to say tu unless there is emphasis or contrast.

For example:

• Vull que apaguis la llum = normal
• Vull que tu apaguis la llum = more emphatic, like I want you to turn off the light

Possibly, but the meaning shifts slightly.

• quan surtis del pis = when you leave/go out of the apartment
• quan marxis del pis = when you go away/leave the apartment
• quan deixis el pis can sound more like when you give up / vacate / leave behind the apartment, depending on context

So sortir del pis is a very natural choice if you mean physically going out the door.

If you are simply reminding someone to switch off the light as they go out, quan surtis del pis is probably the most straightforward option.

Yes, that is also correct.

Both are natural:

• Vull que apaguis la llum quan surtis del pis.
• Quan surtis del pis, vull que apaguis la llum.

The difference is mainly one of emphasis:

• Starting with Vull que... highlights the speaker’s wish.
• Starting with Quan surtis del pis... highlights the time condition first.

Catalan is fairly flexible here.

Vull is the 1st person singular present indicative of voler (to want).

So:

• vull = I want

This verb is irregular. Some present forms are:

• jo vull
• tu vols
• ell/ella vol
• nosaltres volem
• vosaltres voleu
• ells/elles volen

So the full structure is:

• Vull = main verb in the present indicative
• que apaguis = subordinate clause in the present subjunctive
• quan surtis del pis = time clause, also using the subjunctive because it refers to a future event

Usually, pis is best translated as apartment or flat.

For a native English speaker:

• British English: flat
• American English: apartment

So del pis means of/from the flat/apartment.

Just note that in other contexts pis can also have other meanings in Catalan, but in everyday housing vocabulary, un pis very commonly means an apartment/a flat.