La profesora corrigió mis errores con cariño y me habló con tanto respeto que me calmé.

Because la profesora refers to a specific teacher: the teacher.

In Spanish, professions and roles often take the definite article when you are talking about a particular person:

• La profesora = the teacher
• El médico = the doctor

But when directly addressing the person, the article usually disappears:

• Profesora, tengo una duda.

So in this sentence, la profesora is the normal choice.

The verb is corregir. In the preterite, it has a stem change in the third-person forms:

• yo corregí
• tú corregiste
• él/ella corrigió
• ellos/ellas corrigieron

So corrigió is the correct form, not corregió.

This is one of those verbs where e changes to i in the third person of the preterite.

They are in the preterite because the sentence tells a sequence of completed actions:

• she corrected
• she spoke to me
• I calmed down

The preterite is the normal tense for finished events in a story.

If the sentence were describing background, habit, or an ongoing situation, Spanish would be more likely to use the imperfect instead.

Because errores is plural, so the possessive must also be plural:

• mi error = my error
• mis errores = my errors

The possessive adjective agrees with the noun in number.

Because in Spanish, a possessive like mi, mis, tu, sus usually replaces the article before the noun.

So you say:

• mis errores

not:

• los mis errores

That structure is not standard here.

Literally, it means with affection or with fondness, but in many contexts it is better understood as:

• kindly
• gently
• warmly
• in a caring way

So it is not necessarily romantic. Here it suggests that the teacher corrected the mistakes in a kind, considerate way.

Because hablar can take an indirect object when you say who someone spoke to.

• Me habló = she spoke to me
• Te habló = she spoke to you
• Nos habló = she spoke to us

So me means to me here.

It is not reflexive in this case. It is an indirect object pronoun.

This is a very common Spanish pattern:

• tanto/a/os/as + noun + que = so much / so many ... that

Here:

• con tanto respeto que me calmé
  = with so much respect that I calmed down

It expresses a result: her respectful way of speaking had the result that the speaker calmed down.

Because tanto is used before nouns, while tan is used before adjectives and adverbs.

Compare:

• tanto respeto = so much respect
• tan respetuosa = so respectful
• tan bien = so well

Since respeto is a noun, tanto is the right form.

Because here respeto is an abstract, uncountable idea, just like respect in English.

So tanto respeto means so much respect.

A plural like respetos would usually sound different in meaning and is not what you want here.

Yes. Here the verb is calmarse, which means to calm down or to become calm.

• me calmé = I calmed down

Without me, calmé would normally be transitive:

• calmé al niño = I calmed the child

So the reflexive pronoun shows that the change happened to the speaker.

Here que means that and introduces the result clause.

The structure is:

• tanto ... que ... = so much ... that ...

So:

• me habló con tanto respeto que me calmé
  = she spoke to me with so much respect that I calmed down

This que is not meaning because.

The accents help mark the correct stress and distinguish these preterite forms.

For example:

• habló = he/she spoke
• hablo = I speak

And:

• calmé = I calmed down / I calmed
• calme could be read differently and is not the same form

So the written accents are important grammatical markers, not just pronunciation guides.

Yes, Spanish has some flexibility in word order, especially with pronouns and phrases like con cariño.

For example, you could also say:

• La profesora me habló con tanto respeto que me calmé.

That still sounds natural.

But the original version is very smooth because it presents the actions in order:

1. she corrected my mistakes
2. she spoke to me respectfully
3. I calmed down

So the word order supports the flow of the sentence nicely.