L'application propose de courtes séances qu'elle peut écouter sans que son téléphone ne s'allume.

In the plural, French normally uses des for an indefinite noun:

• L'application propose des séances. – The app offers sessions.

But when the noun is preceded by an adjective, des usually becomes de:

• de courtes séances
• de belles histoires
• de longues journées

So the pattern is:

• des + noun → des séances
• des + adjective + noun → de courtes séances

That is why we get de courtes séances, not des courtes séances.

Here proposer means to offer (or to provide), not to propose in the sense of to put forward an idea.

Common patterns with proposer:

1. proposer quelque chose

   • L'application propose de courtes séances.
     The app offers short sessions.

2. proposer de + infinitif

   • L'application propose d'écouter de courtes séances.
     The app suggests/offers listening to short sessions.

3. proposer à quelqu'un de + infinitif

   • L'application lui propose d'écouter de courtes séances.
     The app offers her to listen to short sessions.

In your sentence it follows pattern 1: proposer + direct object (de courtes séances).

Grammatically, elle could refer to any feminine singular noun mentioned in the wider context. In this isolated sentence, we see two possible feminine nouns:

• l'application (feminine)
• an implied woman previously mentioned (for example une utilisatrice)

Logically, écouter des séances is something a person does, not something an app does. So in normal, natural context:

• elle = the female user (the woman who uses the app), not the app itself.

If the writer really wanted elle to refer clearly to l'application, they would usually choose a wording that makes that interpretation more obvious.

Choose between qui and que based on the grammatical role:

• qui = subject of the verb in the relative clause
• que = direct object of the verb in the relative clause

Look at qu'elle peut écouter:

• elle is the subject of peut écouter
• écouter needs a direct object (what is she listening to?)
• The thing listened to is séances

So in the relative clause:

• subject = elle
• direct object = que (referring back to séances)

Therefore:

• les séances qu'elle peut écouter = the sessions that she can listen to
• not les séances qui elle peut écouter, which would be ungrammatical.

The conjunction sans que (without …) almost always requires the subjunctive mood in French:

• sans que + subjunctive

It introduces something that is not happening (a prevented or avoided situation), which is a typical trigger for the subjunctive.

So:

• sans que son téléphone s'allume → the verb s'allume is in the present subjunctive.
  (For il/elle, the form of the present subjunctive of s'allumer happens to be the same as the present indicative: qu'il/elle s'allume.)

Other common sans que + subjunctive examples:

• Il est parti sans que je le voie. – He left without me seeing him.
• Elle est sortie sans que ses parents le sachent. – She went out without her parents knowing.

This ne is called ne explétif (sometimes ne littéraire):

• It does not create a real negation by itself.
• It is often optional.
• It appears after certain conjunctions like sans que, avant que, de peur que, à moins que, etc., especially when there is an idea of prevention, fear, or restriction.

So:

• sans que son téléphone ne s'allume
• sans que son téléphone s'allume

Both mean the same thing: without her phone lighting up.

The ne here:

• does not mean not in the strict grammatical sense;
• is more of a stylistic/idiomatic element.

In everyday spoken French many people simply omit it: sans que son téléphone s'allume is perfectly correct and very common.

Yes, it is optional, and yes, sans que son téléphone s'allume is correct.

• With ne explétif: sans que son téléphone ne s'allume
• Without it: sans que son téléphone s'allume

Both are grammatically acceptable. In modern spoken French, leaving ne out is more common; including it sounds a bit more formal or written.

French distinguishes between:

• allumer quelque chose = to turn something on (transitive)
  
  • Elle allume son téléphone. – She turns her phone on.
• s'allumer = to come on, to light up by itself (intransitive, reflexive form)
  
  • Le téléphone s'allume. – The phone lights up / turns on.

In your sentence, the phone is the thing that becomes lit up; nobody is explicitly doing the action to it. So French uses:

• son téléphone s'allume – her phone turns on / lights up

Son téléphone allume would be wrong here, because it would mean the phone is turning something else on.

Difference in meaning:

• écouter = to listen (to) – an intentional action
• entendre = to hear – something that happens to you, not necessarily intentional

Here, she is listening to short sessions (on an app), which is voluntary, active. So French uses écouter:

• qu'elle peut écouter – that she can listen to

If you used entendre, the meaning would shift toward just hearing them, which is not what is usually meant in the context of audio sessions, podcasts, meditations, etc.

In standard French, de courtes séances is the correct form. Des courtes séances is generally considered incorrect or at least non‑standard.

Rule:

• Plural indefinite article des becomes de before an adjective placed before the noun:
  
  • des séances → de courtes séances
  • des histoires → de belles histoires

So you should say:

• L'application propose de courtes séances.

You would keep des if the adjective comes after the noun:

• L'application propose des séances courtes.

Both de courtes séances and des séances courtes are correct; they just differ in word order and slightly in emphasis.

No, you cannot drop que here. French requires a relative pronoun to connect the noun séances with the clause elle peut écouter.

Correct:

• L'application propose de courtes séances qu'elle peut écouter…

Wrong:

• L'application propose de courtes séances elle peut écouter…

Without que, elle peut écouter becomes an independent clause, creating a run‑on that is ungrammatical in French. The que is needed to say the sessions that she can listen to.

The possessive son agrees with the gender of the noun possessed, not with the owner:

• téléphone is masculine → son téléphone
• voiture is feminine → sa voiture
• écouteurs is plural → ses écouteurs

So son téléphone could mean:

• her phone
• his phone
• its phone

In context:

• Since elle most naturally refers to a female user, son téléphone is naturally understood as her phone.

Only the broader context (who elle is) tells you whether it is his, her, or its; the word son alone does not decide the owner’s gender.