Depois da reunião, eu vou voltar a sorrir.

Because de + a contracts to da in Portuguese.

• de = of/from/after, depending on the structure
• a reunião = the meeting
• depois de a reunião becomes depois da reunião

This kind of contraction is very common:

• de + o = do
• de + a = da
• de + os = dos
• de + as = das

So depois da reunião is the normal form.

Because reunião is a feminine noun: a reunião.

This is something learners often notice because nouns ending in -ão are often masculine, but not always. So you simply have to learn this one as feminine:

• a reunião
• da reunião
• uma reunião

You can leave it out.

Portuguese often drops subject pronouns when the verb already makes the subject clear. So both of these are natural:

• Depois da reunião, eu vou voltar a sorrir.
• Depois da reunião, vou voltar a sorrir.

Adding eu can give a little more emphasis, contrast, or clarity.

Brazilian Portuguese very often uses ir + infinitive to talk about the future.

So:

• eu vou voltar a sorrir = natural, everyday Brazilian Portuguese
• eu voltarei a sorrir = also correct, but more formal or literary

For most everyday speech, vou + infinitive is the most common choice.

This is an important structure. Voltar a + infinitive means to do something again or to resume doing something.

So:

• voltar a sorrir = to smile again / to start smiling again

Here voltar does not mean physically to return somewhere. It means returning to an action or state.

Other examples:

• voltei a estudar = I started studying again
• ela voltou a trabalhar = she went back to working

Because after voltar in this meaning, Portuguese uses the pattern voltar a + infinitive.

So the standard structure is:

• voltar a sorrir
• voltar a estudar
• voltar a falar

That a is part of the verbal pattern. It is not optional here.

Yes. Depois da reunião, vou sorrir de novo is correct and natural.

But there is a slight nuance:

• vou sorrir de novo = I’ll smile again
• vou voltar a sorrir = I’ll go back to smiling / I’ll smile again after a period of not smiling

So voltar a sorrir often suggests a return to a previous emotional state or habit.

Because they mean different things:

• sorrir = to smile
• rir = to laugh

So:

• voltar a sorrir = smile again
• voltar a rir = laugh again

They are related, but not interchangeable.

It is very natural and usually preferred here because Depois da reunião is a time expression placed at the beginning of the sentence.

So the comma helps separate the introductory phrase from the main clause:

• Depois da reunião, eu vou voltar a sorrir.

In very informal writing, some people may leave it out, but using the comma is the safer and more standard choice.

Yes. Portuguese allows some flexibility.

These are both natural:

• Depois da reunião, eu vou voltar a sorrir.
• Eu vou voltar a sorrir depois da reunião.

The difference is mostly emphasis:

• Starting with Depois da reunião highlights when
• Putting it at the end makes the sentence feel a little more neutral

When depois is followed by a noun or noun phrase, yes: it normally uses de.

Examples:

• depois da aula = after class
• depois do almoço = after lunch
• depois da reunião = after the meeting

But when depois appears alone, there is no de:

• Te ligo depois. = I’ll call you later.

So in your sentence, de is needed because reunião follows it.

In Brazilian Portuguese, the stress is on the last syllable: reu-ni-ÃO.

A rough English-friendly approximation is:

• heh-oo-nee-OW̃

A few useful points:

• the r at the beginning of reunião is usually pronounced like an English h in Brazilian Portuguese
• -ão is a nasal sound, very common in Portuguese
• the written accent ã/o pattern helps show the stressed nasal ending

So the word sounds roughly like heh-oo-nee-owng, but nasalized, not fully like an English ng.

Yes, almost.

• Depois da reunião = after the meeting
• Após a reunião = after the meeting

But após is usually a bit more formal or written-sounding. In everyday Brazilian Portuguese, depois de is more common in normal conversation.