Vou responder ao e-mail e deixar um recado para o gerente.

In Brazilian Portuguese, ir + infinitive is a very common way to talk about the near future.

• vou responder = I’m going to answer / I will answer
• vou deixar = I’m going to leave / I will leave

So vou is the present tense of ir (to go), but here it works like a future marker, not a literal movement verb.

A more formal one-word future would be:

• responderei
• deixarei

But in everyday speech, vou responder and vou deixar are much more common.

Because both actions have the same subject (I) and the same future idea.

So:

• Vou responder ao e-mail e deixar um recado...

means:

• I’m going to answer the email and leave a message...

In English, this works the same way:

• I’m going to answer the email and leave a message

You do not need to repeat vou before deixar, although you could in some contexts for emphasis:

• Vou responder ao e-mail e vou deixar um recado...

That is grammatically fine, but less economical.

Ao is a contraction of:

• a + o = ao

So:

• ao e-mail = literally to the email

Portuguese very often combines a preposition with the definite article.

Other common contractions are:

• a + a = à
• de + o = do
• de + a = da
• em + o = no
• em + a = na

In this sentence, ao e-mail appears because the verb is being used with the preposition a plus the masculine article o.

Both forms can be heard in Brazilian Portuguese, but responder ao e-mail sounds very natural and is often felt to be more careful or standard.

With responder, Portuguese may use:

• responder a algo/alguém
• or, in many everyday contexts, responder algo

So a Brazilian might say either:

• Vou responder ao e-mail
• Vou responder o e-mail

The version in your sentence uses the preposition a, which contracts with o to become ao.

For a learner, responder ao e-mail is a very safe and natural choice.

Yes. In Brazilian Portuguese, e-mail is normally treated as a masculine noun:

• o e-mail
• um e-mail
• os e-mails

That is why you get ao e-mail and not à e-mail.

You may also see email written without the hyphen. Both spellings are used, though e-mail is still very common.

Deixar um recado is a very common expression meaning:

• to leave a message
• sometimes to leave a note

Literally:

• deixar = to leave
• recado = message / note

A recado is often a message intended for someone who is not available at the moment.

For example:

• Posso deixar um recado? = Can I leave a message?
• Deixei um recado para ela. = I left a message for her.

Because deixar um recado para alguém is the usual way to say leave a message for someone.

Here, para shows the intended recipient:

• um recado para o gerente = a message for the manager

Using ao gerente would not be the normal phrasing with deixar um recado.

So the natural pattern is:

• deixar um recado para + person

Examples:

• deixar um recado para a Ana
• deixar um recado para o médico
• deixar um recado para o gerente

This is about definite and indefinite articles.

• um recado = a message
  This is indefinite: it is just some message, not a previously identified one.

• o gerente = the manager
  This is definite: it refers to a specific manager, probably the one relevant in that situation.

So the sentence is saying:

• I’m going to answer the email and leave a message for the manager

not:

• ...leave the message for a manager

Yes. In many contexts, vou responder can be translated either way.

Portuguese ir + infinitive often covers both ideas:

• a planned future
• an intended future
• a simple future action

So depending on context, you might translate it as:

• I’m going to answer the email
• I’ll answer the email

The Portuguese sentence itself does not force a big distinction between those two English options.

Not exactly.

Gerente usually means manager, someone who manages a department, store, office, bank branch, etc.

It does not automatically mean boss in the broad English sense.

Examples:

• gerente do banco = bank manager
• gerente da loja = store manager

If you mean boss more generally, Portuguese often uses:

• chefe
• patrão / patroa in some contexts

So here, o gerente is best understood as the manager.

A simple pronunciation guide would be:

• Vou responder ao e-mail e deixar um recado para o gerente.
• roughly: voh hoo-pon-DER ow ee-MAYL ee day-SHAR oong heh-KAH-doo PAH-rah oo zheh-REN-chee

A few helpful notes:

• vou sounds roughly like voh
• responder has stress on the last syllable: responDER
• ao sounds like ow
• e-mail is pronounced close to the English word, though adapted to Portuguese rhythm
• deixar sounds like day-SHAR
• recado has stress on ca: re-CA-do
• gerente usually sounds like zhe-REN-chee in Brazil

Pronunciation varies a bit by region, but this will be widely understood.

Yes. That would also be perfectly natural.

Changes:

• responder o e-mail instead of responder ao e-mail
• uma mensagem instead of um recado

These are all possible in Brazilian Portuguese.

Very roughly:

• recado often feels like message / note left for someone
• mensagem is a broader word for message

So your original sentence is natural, and this alternative is natural too.