Le pedí perdón a mi hermana por olvidar su libro.

Because Spanish very often uses an indirect object pronoun together with the full noun.

• le = to her
• a mi hermana = to my sister

So Le pedí perdón a mi hermana literally works like:

• To her, I asked forgiveness — to my sister

In natural English we would not usually repeat this idea, but in Spanish this is very common, especially with people. It is called clitic doubling.

So here le is not extra in a strange way; it is a normal Spanish pattern.

Pedir perdón is a very common expression meaning:

• to ask for forgiveness
• more naturally in English: to apologize

So:

• Le pedí perdón a mi hermana = I asked my sister for forgiveness
• natural translation: I apologized to my sister

Even though English usually says apologize, Spanish often uses pedir perdón.

Because pedir means to ask for / to request, while preguntar means to ask a question.

Here the speaker is not asking a question. They are asking for forgiveness.

So:

• pedir perdón = to ask for forgiveness
• preguntar would not fit here

Also note:

• pedí is the preterite form of pedir
• it means I asked or I apologized

Pedí is the first-person singular preterite of pedir.

• yo pedí = I asked / I apologized

The preterite is used for a completed action in the past. So this sentence presents the apology as a finished event.

Compare:

• Le pedí perdón = I apologized to her / one completed action
• Le pedía perdón = I was apologizing to her or I used to apologize to her / ongoing or repeated in the past

So pedí is the natural choice if you mean one specific apology.

Because por + infinitive is a common way to express the reason for something.

Here:

• por olvidar su libro = for forgetting her book

So the structure is:

• pedir perdón por + infinitive
• to apologize for + -ing form

Examples:

• Perdón por llegar tarde = Sorry for arriving late
• Le pedí perdón por mentir = I apologized to him/her for lying

In English we often use for + -ing, and Spanish often uses por + infinitive.

Because after por, Spanish often uses the infinitive when the action is being expressed in a general verbal way.

So:

• por olvidar su libro = for forgetting her book

This is similar to English:

• for forgetting not
• for I forgot

If you wanted a full clause instead, you would need a different structure, for example:

• porque olvidé su libro = because I forgot her book

So both can work, but they are different structures:

• por + infinitive → compact, common after expressions like pedir perdón
• porque + finite verb → full clause with a conjugated verb

By default, most learners will understand that the speaker forgot the book.

So the sentence normally means:

• I apologized to my sister for forgetting her book

That is because in por olvidar su libro, the infinitive olvidar usually connects naturally to the subject of the main verb, which here is I.

If you wanted to make it clear that the sister forgot the book, Spanish would usually say it more explicitly, for example:

• Le pedí perdón a mi hermana porque ella olvidó su libro
• Le pedí perdón a mi hermana por haber olvidado ella su libro
  (more formal / less common in everyday speech)

So in the original sentence, the most natural reading is that I forgot it.

Yes, su can be ambiguous.

It can mean:

• his
• her
• your (formal singular)
• their

So su libro could theoretically mean:

• her book
• his book
• their book
• etc.

But in this sentence, because a mi hermana appears right before it, most people will understand su libro as my sister’s book.

If you want to make it completely clear, you could say:

• el libro de mi hermana = my sister’s book

So:

• Le pedí perdón a mi hermana por olvidar el libro de mi hermana

That is clearer, but it sounds more repetitive. Spanish often relies on context instead.

Because mi hermana is the indirect object of the verb phrase pedir perdón.

You are asking forgiveness to someone, and Spanish marks that person with a:

• Le pedí perdón a mi hermana
• literally: I asked forgiveness to my sister

This a is not the personal a used with direct objects; here it is part of how Spanish marks the indirect object.

Compare:

• Di el libro a mi hermana = I gave the book to my sister
• Le pedí perdón a mi hermana = I asked my sister for forgiveness

Yes. That is another natural way to express the same idea.

• Me disculpé con mi hermana por olvidar su libro

This also means:

• I apologized to my sister for forgetting her book

A small nuance:

• pedir perdón focuses on asking forgiveness
• disculparse focuses more directly on apologizing

In many everyday situations, both are fine.

Because mi hermana is not the direct object here; it is the indirect object.

Spanish indirect object pronouns are:

• me
• te
• le
• nos
• os
• les

So for to my sister, you use:

• le

Not:

• la, which is a direct object pronoun

Compare:

• La vi = I saw her
  Here her is the direct object.
• Le pedí perdón = I asked her for forgiveness
  Here her is the indirect object.

That is why le is correct.

Yes, somewhat. Spanish allows some flexibility, though not every version sounds equally natural.

The original:

• Le pedí perdón a mi hermana por olvidar su libro

is very natural.

You could also hear:

• A mi hermana le pedí perdón por olvidar su libro

This puts more emphasis on a mi hermana.

But some orders are less natural in ordinary speech. For a learner, the original version is a very good model to follow:

• indirect object pronoun + verb + perdón + a + person + por + infinitive

You could do a literal translation, but it would sound less natural in English.

Word-for-word-ish:

• To her I asked forgiveness, to my sister, for forgetting her book

A closer literal translation:

• I asked my sister for forgiveness for forgetting her book

Natural English:

• I apologized to my sister for forgetting her book

So this is a good example of a sentence where understanding the Spanish structure is useful, but translating too literally is not the best final English version.