Её глубокий вздох сказал мне больше, чем длинное объяснение.

Here её means her in the possessive sense: her deep sigh.

Russian её can also mean her as an object pronoun, but in this sentence it comes directly before a noun (вздох), so it clearly means her = belonging to her.

A useful thing to remember: as a possessive word, её does not change its form:

• её брат = her brother
• её книга = her book
• её друзья = her friends

Because adjectives in Russian agree with the noun they describe.

Here глубокий describes вздох, and вздох is:

• masculine
• singular
• nominative

So the adjective also has to be masculine singular nominative: глубокий.

Compare:

• глубокий вздох — masculine
• глубокая пауза — feminine
• глубокое чувство — neuter
• глубокие мысли — plural

Yes. Глубокий вздох is a very natural way to say a deep sigh.

Russian uses глубокий not only for things that are literally deep, but also for breaths, sighs, thoughts, feelings, and so on. So this phrase sounds completely normal.

Because Russian past tense agrees with the subject in gender and number.

The subject here is вздох (sigh), and вздох is masculine singular. So the verb is сказал.

Compare:

• вздох сказал — the sigh told/said
• пауза сказала — the pause told/said
• слова сказали — the words told/said

Yes — metaphorically, absolutely.

This works the same way as in English sentences like:

• Her silence said everything.
• His face told me the truth.

So Её глубокий вздох сказал мне... is a natural figurative way to say that the sigh communicated something very clearly.

Because сказать uses the dative for the person who receives the message.

The pattern is:

сказать кому? — to say/tell to whom?

So:

• мне = to me
• тебе = to you
• ему = to him
• нам = to us

That is why сказал мне means told me or said to me.

Because сказать and говорить are different aspects.

• сказать = perfective, a single completed act of saying
• говорить = imperfective, speaking in general, repeatedly, or as a process

A sigh is one momentary act that communicates something, so сказал is the natural choice.

If you used говорил, it would sound more like an ongoing or repeated act of speaking, which does not fit a single sigh very well.

It means more than.

In this sentence, больше means to a greater degree or more strongly, not a larger amount of some noun.

So the idea is:

Her deep sigh told me more than a long explanation.

This is different from sentences like:

• больше воды = more water
• больше времени = more time

There, больше means more of something. Here it is part of a comparison: больше, чем...

Because чем introduces the second part of the comparison.

In a sentence like this, standard Russian punctuation uses a comma:

больше, чем длинное объяснение

The comma helps mark the comparison clearly: more than a long explanation.

Because Russian often leaves out repeated words when the meaning is obvious.

The full idea is something like:

Её глубокий вздох сказал мне больше, чем длинное объяснение [сказало бы мне].

But repeating the verb would be unnecessary, so Russian simply omits it.

English does the same thing:

• Her deep sigh told me more than a long explanation [would have].

For a learner, the important thing is that объяснение is neuter and inanimate, so its nominative and accusative forms look the same:

• nominative: длинное объяснение
• accusative: длинное объяснение

In this sentence it appears as the second part of the comparison after чем, so you can think of it as shorthand for:

than a long explanation [would have told me]

That is why you see the plain form длинное объяснение.

This is a natural, neutral word order.

Russian word order is flexible, but it is very common to put the possessive word first and then the adjective:

её глубокий вздох = her deep sigh

Other word orders are possible, but they would usually change the emphasis or sound more literary. For a normal neutral sentence, Её глубокий вздох is exactly what you would expect.

In careful writing, yes, ё is the correct letter here.

However, in many real Russian texts, people often write ее instead of её. Native speakers usually understand it from context, but for learners it is much better to pay attention to ё, because it affects pronunciation.

So:

• written carefully: её
• often seen in ordinary texts: ее
• pronunciation: still её with yo sound