Перед тем как ответить начальнице, я решила сначала вздохнуть и успокоиться.

Перед тем как means before or more literally before the moment when.

It introduces an action that happens earlier than the main action:

• Перед тем как ответить начальнице... = Before answering the boss...
• я решила... = I decided...

This is a very common Russian way to say before doing something.

A rough word-for-word breakdown is:

• перед = before
• тем = that / that thing / that moment
• как = how / when in this fixed expression

But in real usage, you should learn перед тем как as one chunk meaning before.

Because Russian often uses an infinitive after перед тем как when English would say before doing something.

So:

• Перед тем как ответить начальнице = Before answering the boss
• literally: Before to-answer the boss

Russian could also use a full clause in some contexts, but the infinitive is very natural here because the subject is the same person in both parts:

• я решила...
• and я is also the one who will ответить

That makes the infinitive structure compact and natural.

This is about aspect.

• ответить = perfective, a completed single reply
• отвечать = imperfective, the process / repeated action / general answering

Here the speaker means one completed action: to give a reply. So ответить is the natural choice.

Compare:

• Перед тем как ответить начальнице... = before replying to the boss
• Я часто отвечала начальнице спокойно. = I often answered the boss calmly

In this sentence, the idea is not the process of answering, but the one act of replying.

Начальнице is in the dative case.

The verb ответить takes the person you reply to in the dative:

• ответить кому? = reply to whom?

So:

• ответить начальнице = reply to the female boss

Some examples:

• ответить другу = reply to a friend
• ответить маме = reply to mom
• ответить преподавателю = reply to the teacher

The dictionary form is начальница. Its dative singular form is начальнице.

Yes, it matters.

• начальник = male boss / chief
• начальница = female boss

Since the sentence says начальнице, we know the person being answered is a woman.

This does not tell us by itself whether the speaker is male or female. That comes from решила, which is feminine.

In the past tense, Russian verbs agree with the subject in gender and number.

The subject is я, but in Russian past tense я does not show gender by itself. The verb does:

• я решил = I decided (male speaker)
• я решила = I decided (female speaker)
• мы решили = we decided

So решила tells us the speaker is female.

Because they depend on решила.

Russian uses решить + infinitive to say decide to do something:

• решила вздохнуть = decided to sigh / take a breath
• решила успокоиться = decided to calm down

Since the speaker decided to do two things, the infinitives are joined by и:

• решила сначала вздохнуть и успокоиться

This is very similar to English decided to take a breath and calm down.

The -ся here shows that the action comes back to the subject: to calm oneself down / to become calm.

Compare:

• успокоить кого-то = to calm someone down
• успокоиться = to calm down

So:

• Я успокоила ребёнка. = I calmed the child down.
• Я успокоилась. = I calmed down.

In your sentence, the speaker wants to calm herself down before replying, so успокоиться is exactly right.

Yes. Сначала means first, at first, or to begin with, depending on context.

Here it means that before answering, the speaker wanted to do something first:

• я решила сначала вздохнуть и успокоиться
  = I decided to first take a breath and calm down

It emphasizes sequence:

1. take a breath / calm down
2. answer the boss

So сначала helps show that the reply will come only after that pause.

Yes, вздохнуть literally means to sigh or to take a breath.

In this sentence, it probably suggests a deliberate pause to compose oneself. In English, depending on context, you might translate it as:

• to sigh
• to take a breath
• to breathe deeply

Because the sentence also has успокоиться, the overall idea is emotional self-control: the speaker pauses, breathes, and calms down before responding.

Because Перед тем как ответить начальнице is an introductory subordinate clause, and the main clause comes after it:

• Перед тем как ответить начальнице,
• я решила сначала вздохнуть и успокоиться.

In English, this is similar to:

• Before answering the boss, I decided...

Russian normally separates that fronted subordinate clause from the main clause with a comma.

Because here перед тем как functions as one conjunction-like unit meaning before.

So the sentence is written as:

• Перед тем как ответить начальнице, я решила...

Learners often expect a comma before как, because literally the phrase looks like several separate words. But in this use, Russian usually treats перед тем как as a fixed expression introducing the whole subordinate clause.

The important comma here is the one that separates the subordinate clause from the main clause.

Yes, Russian word order is flexible.

The sentence as written is very natural:

• Перед тем как ответить начальнице, я решила сначала вздохнуть и успокоиться.

But other versions are possible, with slightly different emphasis:

• Перед тем как ответить начальнице, я сначала решила вздохнуть и успокоиться.
• Я решила, перед тем как ответить начальнице, сначала вздохнуть и успокоиться.

The original sounds smooth and neutral. Placing сначала before the infinitives makes it clear that taking a breath and calming down happens before the reply.

Grammatically, they are two separate infinitives joined by и:

• вздохнуть = take a breath / sigh
• успокоиться = calm down

But semantically they work together as one preparation before answering. The first action helps lead into the second.

So the sentence suggests something like:

• pause,
• breathe,
• regain composure,
• then reply.

That combination is very natural in Russian.

Yes, that is close to the Russian structure.

A more natural English version might be:

• Before replying to my boss, I decided to take a breath and calm down first.
• Before answering the boss, I decided to pause, take a breath, and calm down.

The key grammar points behind the Russian are:

• Перед тем как = before
• ответить начальнице = reply to the female boss
• я решила = I decided (female speaker)
• вздохнуть и успокоиться = take a breath and calm down

So your more literal version is grammatically reasonable, even if smoother English would phrase it a bit differently.