Nous attendons quelques minutes pour que la tarte refroidisse avant de la servir.

Because pour que introduces a clause with its own subject and verb: la tarte refroidisse.

• pour + infinitive is used when the subject stays the same

  • Nous attendons quelques minutes pour servir la tarte.
    = We wait a few minutes in order to serve the tart.

• pour que + subjunctive is used when there is another finite verb after it

  • Nous attendons quelques minutes pour que la tarte refroidisse.
    Literally: We wait a few minutes so that the tart cools down.

So here, French treats the tart cooling as a full clause, which is why que is needed.

Because pour que normally requires the subjunctive in French.

The subjunctive is often used after expressions of:

• purpose
• desire
• necessity
• emotion
• doubt

Here, pour que expresses purpose: we are waiting so that the tart can cool down.

So:

• refroidit = indicative
• refroidisse = subjunctive

This is a standard grammar pattern:

• Je ferme la fenêtre pour qu’il fasse moins froid.
• Nous partons tôt pour que tout soit prêt.

Refroidisse is a subjunctive form of refroidir.

The verb is refroidir = to cool, to cool down.

Present subjunctive of refroidir:

• que je refroidisse
• que tu refroidisses
• qu’il/elle refroidisse
• que nous refroidissions
• que vous refroidissiez
• qu’ils/elles refroidissent

In your sentence, the subject is la tarte, which is third-person singular, so the form is refroidisse.

Because after avant, French uses two different patterns:

• avant de + infinitive when there is no new finite verb
• avant que + subjunctive when a full clause follows

In your sentence:

• avant de la servir = before serving it

That uses an infinitive, so de is required.

Compare:

• Nous attendons avant de servir la tarte.
• Nous attendons avant que la tarte ne refroidisse complètement.

So avant de is the normal choice here because the second action is expressed with servir, an infinitive.

La is a direct object pronoun replacing la tarte.

Earlier in the sentence, you have la tarte. To avoid repeating it, French uses the pronoun la:

• servir la tarte
• la servir = serve it

So:

• avant de servir la tarte = before serving the tart
• avant de la servir = before serving it

Because tarte is feminine singular, the pronoun is la.

In French, object pronouns usually come before the verb they belong to, even when that verb is in the infinitive.

So:

• servir la tarte → la servir
• manger le gâteau → le manger
• voir Marie → la voir

That is why French says:

• avant de la servir

and not:

• avant de servir la

Quelques is a determiner meaning some or a few, so it directly modifies the noun:

• quelques minutes
• quelques jours
• quelques personnes

You do not need:

• de
• des
• another article

So quelques minutes simply means a few minutes or some minutes.

French often uses the present tense to describe:

• habitual actions
• general instructions
• what is happening now

So Nous attendons quelques minutes... can mean:

• We wait a few minutes...
• We are waiting a few minutes...

In context, it may sound like:

• a general cooking instruction
• a description of what we do before serving the tart

French uses the simple present more broadly than English sometimes does.

Yes. In everyday spoken French, on often replaces nous.

So a very natural spoken version would be:

• On attend quelques minutes pour que la tarte refroidisse avant de la servir.

Both are correct:

• nous = a bit more formal or neutral
• on = very common in conversation

The meaning is the same here.

Here, refroidir means to cool down.

It can be:

• transitive: to cool something
• intransitive: to become cool / cool down

Examples:

• Je refroidis la soupe. = I cool the soup.
• La soupe refroidit. = The soup cools down.

In your sentence, it is used intransitively:

• la tarte refroidisse = the tart cool down

The order is very typical French:

• Nous attendons quelques minutes = main clause
• pour que la tarte refroidisse = purpose clause
• avant de la servir = time sequence, what happens later

So the structure is:

main action + purpose + before + infinitive action

French often builds sentences this way when explaining a process or giving instructions.

The original sentence is already natural, but in everyday speech you might hear:

• On attend quelques minutes pour que la tarte refroidisse avant de la servir.

You might also hear a simpler phrasing such as:

• On attend quelques minutes avant de servir la tarte, pour qu’elle refroidisse.

The original version is perfectly correct and clear, though, especially in written or instructional French.

Yes. Avant que is followed by the subjunctive.

For example:

• avant que la tarte refroidisse
• avant qu’il parte
• avant que nous commencions

So in this sentence:

• pour que → subjunctive
• avant de → infinitive

That contrast is useful to remember:

• que often introduces a conjugated verb
• de often introduces an infinitive