Стоит ей услышать музыку, как она сразу начинает улыбаться.

Here стоит comes from стоить, not стоять. It does not mean stands.

In the pattern стоит + dative + infinitive, как ..., it means something like:

it only takes... or as soon as... or one has only to...

So Стоит ей услышать музыку, как... means As soon as she hears music... or more literally It only takes her to hear music for...

Because this construction normally uses the dative for the person involved:

стоит мне...
стоит тебе...
стоит ему / ей...
стоит нам...

So ей means for her in this pattern.

You are not using the normal subject form она here, because the first part is built as an impersonal structure: стоит + dative + infinitive.

Because this is basically a fixed impersonal construction. Стоит stays in the 3rd person singular form and does not agree with the person in the dative.

So you say:

Стоит мне...
Стоит ей...
Стоит им...

The form стоит does not change here to match me, her, or them.

Because after стоит + dative, Russian uses an infinitive:

Стоит ей услышать музыку...

The idea is roughly it only takes for her to hear music...

So the infinitive is required by the structure. You are not saying she hears, but rather building a phrase like for her to hear.

Because услышать is perfective and refers to a single completed event: to hear / catch the sound.

That works well here because the sentence describes a trigger:

the moment she hears music, she starts smiling

If you used слышать, it would sound less natural here, because слышать is imperfective and usually describes ongoing or repeated hearing rather than the moment of noticing or catching the sound.

So:

• услышать музыку = to hear music, to catch the sound
• слышать музыку = to be hearing music / to hear music in general

No. Here как is a conjunction, not the question word how.

In the pattern стоит ..., как ..., it introduces the result that follows immediately. The whole structure means something like:

as soon as ... or no sooner ... than ...

So:

Стоит ей услышать музыку, как она сразу начинает улыбаться.

means:

As soon as she hears music, she immediately starts smiling.

Because the sentence has two parts, and in this construction the comma is standard:

Стоит ей услышать музыку, как она сразу начинает улыбаться.

The first clause sets up the trigger, and the second clause gives the immediate result. Russian punctuation normally separates them with a comma.

Because ей in the first clause is not the grammatical subject of the second clause.

In the second clause, you have a normal finite verb:

она начинает улыбаться

That clause needs a subject in the nominative, so она appears.

Russian could sometimes omit the pronoun if the subject is clear from context, but here keeping она makes the sentence explicit and natural.

Начинает улыбаться means starts smiling, so it highlights the beginning of the reaction.

That matches the idea of an immediate response to hearing music.

If you said она сразу улыбается, that would also be understandable, but it is a bit less focused on the moment the smile begins.

So the difference is roughly:

• начинает улыбаться = starts to smile
• улыбается = smiles

The original version emphasizes the quick onset of the smile.

Because музыку is the direct object of услышать.

You hear what?
музыку

So Russian uses the accusative:

• nominative: музыка
• accusative: музыку

This is just normal object marking after the verb услышать.

Be careful: Ей стоит услышать музыку is understood differently.

That usually means something like:

She should hear the music or It would be worth it for her to hear the music

So the word order matters a lot. Compare:

• Стоит ей услышать музыку, как... = As soon as she hears music...
• Ей стоит услышать музыку = She should hear the music / It would be worth her hearing the music

Same verb, but a different construction and a different meaning.

Yes. A simpler, more straightforward version would be:

Когда она слышит музыку, она сразу начинает улыбаться.

or

Как только она слышит музыку, она сразу начинает улыбаться.

These are easier for learners because they use more familiar conjunctions.

The original Стоит ей услышать музыку, как... is a very natural Russian pattern, but it is slightly more literary or stylistically marked than the simplest everyday version.