По её улыбке я сразу догадалась, что у неё есть другая версия этой истории.

Because the speaker is female.

In Russian past tense, verbs agree with gender and number:

• догадался = a man guessed / figured out
• догадалась = a woman guessed / figured out
• догадалось = it figured out (neuter, rare with people)
• догадались = they figured out

So я сразу догадалась tells you that the person speaking is a woman.

По её улыбке literally means something like from her smile, by her smile, or judging by her smile.

The noun улыбка changes to улыбке because the preposition по here requires the dative case.

• улыбка = smile
• по улыбке = by/from the smile, judging by the smile

This pattern is very common in Russian:

• по глазам = by the eyes / from someone’s eyes
• по голосу = by the voice
• по выражению лица = by the facial expression

So По её улыбке я сразу догадалась means I immediately guessed it from her smile.

These are actually two different grammatical words, even though they look related.

1. её in по её улыбке is a possessive pronoun meaning her:

   • её улыбка = her smile

2. неё in у неё есть comes from the personal pronoun она and means something like at her / with her, which is how Russian expresses she has:

   • у неё есть = she has

Why the н?

After many prepositions, third-person pronouns get an extra н:

• у неё
• к нему
• с ними

But possessive её does not get that н:

• её книга = her book
• её улыбка = her smile

So:

• по её улыбке = by her smile
• у неё есть = she has

Russian usually expresses possession with the pattern:

у + person (genitive) + есть + thing

Literally, it is closer to at someone there is.

So:

• у неё есть другая версия = literally at her there is another version
• natural English: she has another version

This is the normal way to say have in Russian.

More examples:

• у меня есть брат = I have a brother
• у нас есть время = we have time
• у него есть вопрос = he has a question

Often есть is omitted in the present tense when you are talking about possession in a broad sense, but here keeping есть sounds natural and clear.

Догадаться means to guess, to figure out, to infer, or to realize from clues.

In this sentence, the speaker did not just directly understand something. She worked it out from the woman’s smile.

So:

• понять = to understand
• догадаться = to guess/figure out based on signs or clues

That is why по её улыбке fits so well with догадалась:

• From her smile, I figured out...

This combination suggests an inference: the smile gave it away.

Сразу means right away, immediately, or at once.

In я сразу догадалась, it modifies the verb:

• я догадалась = I figured it out
• я сразу догадалась = I figured it out immediately

Russian word order is flexible, but this placement is very natural. You could also hear:

• Я догадалась сразу
• Сразу я догадалась...
  though this sounds more marked or stylistic

The version in the sentence is the most neutral and idiomatic.

Что introduces a subordinate clause, similar to that in English.

• Я догадалась, что... = I figured out that...

So the sentence is structured like this:

• По её улыбке = From her smile
• я сразу догадалась = I immediately figured out
• что у неё есть другая версия этой истории = that she has another version of this story

In English, that is often optional:

• I guessed that she had...
• I guessed she had...

In Russian, что is normally stated explicitly.

Другая means another, different, or a different one.

So другая версия этой истории means:

• another version of this story
• a different version of the story
• idiomatically, a different side of the story

It suggests that the woman sees the events differently, or knows a version that does not match the one already being discussed.

Grammatically:

• другая agrees with версия
• версия is feminine singular
• so the adjective must also be feminine singular: другая

Compare:

• другой человек = another person / a different person
• другое мнение = another opinion / a different opinion
• другая идея = another idea / a different idea

Because версия is followed by the equivalent of of this story, and in Russian that requires the genitive case.

• эта история = this story (nominative)
• этой истории = of this story (genitive)

So:

• версия этой истории = a version of this story

This is a very common pattern:

• конец фильма = the end of the film
• начало книги = the beginning of the book
• часть плана = part of the plan
• версия событий = version of events

Here both words are in genitive:

• этой = genitive feminine singular of эта
• истории = genitive feminine singular of история

In general, история can mean either story or history, depending on context.

But in this sentence, этой истории clearly means this story or this matter / this whole situation, not academic history.

So другая версия этой истории is like saying:

• another version of this story
• another side of the story
• her own version of what happened

No, they are different.

• По её улыбке = judging by her smile / from her smile
• Из-за её улыбки = because of her smile or due to her smile

In this sentence, the idea is not that the smile caused the guessing in a direct causal sense, but that the smile served as a clue.

So по is the correct choice.

Compare:

• По его голосу я понял, что он устал.
  = From his voice, I understood he was tired.

• Из-за его голоса было трудно слушать лекцию.
  = Because of his voice, it was hard to listen to the lecture.

Yes, it is very natural.

Russian allows more flexibility in word order than English, but the original sentence sounds smooth and standard:

По её улыбке я сразу догадалась, что у неё есть другая версия этой истории.

This order works well because:

• По её улыбке sets the clue first
• я сразу догадалась gives the main action
• что... introduces what was guessed

Other orders are possible, but they change emphasis:

• Я сразу догадалась по её улыбке, что...
  Slightly more focus on I immediately figured out

• Что у неё есть другая версия этой истории, я сразу догадалась по её улыбке.
  Grammatically possible, but much more marked and less neutral

So the original is a very good, idiomatic order for everyday Russian.

Yes. In context, it can strongly suggest that the woman disagrees with the current account, or is hiding some alternative interpretation.

In English, depending on tone, you might translate it as:

• another version of the story
• a different version of events
• her own version of the story
• another side to the story

So even though the words are simple, the phrase can imply:

• she knows more
• she disagrees
• the full truth has not been told yet

That kind of nuance is very natural in Russian too.