Mal o bebé deixou de roncar, toda a gente suspirou de alívio.

Here mal is not the adjective/adverb meaning bad/badly.

In this sentence, mal is a conjunction meaning:

• as soon as
• once
• hardly / scarcely ... when (in a more literary or tighter English translation)

So:

• Mal o bebé deixou de roncar, toda a gente suspirou de alívio. = As soon as the baby stopped snoring, everyone sighed with relief.

This use of mal is very common in Portuguese.

No, nothing is missing.

In Portuguese, mal can directly introduce a clause:

• Mal chegou, telefonou.
• Mal acabou de comer, saiu.

So mal + clause is a normal structure meaning as soon as / no sooner ... than.

You do not need que here.

Deixar de + infinitive means to stop doing something or to cease doing something.

So:

• deixou de roncar = stopped snoring

More examples:

• deixei de fumar = I stopped smoking
• ela deixou de estudar = she stopped studying
• eles deixaram de falar um com o outro = they stopped talking to each other

This is a very useful pattern in Portuguese.

Yes, parou de roncar is also correct.

Both mean stopped snoring, but there can be a slight nuance:

• parar de + infinitive = to stop an action
• deixar de + infinitive = to cease doing something

In many everyday sentences, they are interchangeable.

So these are both natural:

• O bebé parou de roncar.
• O bebé deixou de roncar.

Deixar de can sometimes sound a little broader or slightly more formal, but in many contexts the difference is small.

O bebé means the baby, so it refers to a specific baby already known from the context.

• o bebé = the baby
• um bebé = a baby

If the speaker and listener already know which baby is being talked about, Portuguese uses the definite article naturally, just like English often does.

Toda a gente means everyone or everybody.

It is a very common European Portuguese expression.

Although it refers to many people, grammatically it behaves as a singular expression. That is why the verb is singular:

• toda a gente suspirou
  not toda a gente suspiraram

So:

• Toda a gente estava cansada. = Everyone was tired.
• Toda a gente sabe isso. = Everyone knows that.

Because toda a gente is grammatically treated as singular.

This is similar to how English uses everyone is, not everyone are.

So Portuguese says:

• Toda a gente suspirou.
• Toda a gente ficou contente.

Even though the meaning is plural, the grammar is singular.

Suspirar de alívio means to sigh with relief or literally to sigh from relief.

Portuguese often uses de in expressions where English uses with:

• suspirar de alívio = to sigh with relief
• chorar de alegria = to cry with joy
• tremer de medo = to tremble with fear

So de alívio is the normal idiomatic choice here.

Both are in the pretérito perfeito simples in Portuguese grammar, which is the normal past tense used for completed actions.

• deixou = stopped
• suspirou = sighed

The sentence describes two completed events in sequence:

1. the baby stopped snoring
2. everyone sighed with relief

Because mal already shows the immediate sequence, the simple past works very naturally here.

The comma separates the opening subordinate clause from the main clause.

Structure:

• Mal o bebé deixou de roncar, = subordinate time clause
• toda a gente suspirou de alívio. = main clause

This is very common when a time clause comes first:

• Quando chegou, sentou-se.
• Assim que acabou, saiu.
• Mal o bebé deixou de roncar, toda a gente suspirou de alívio.

The comma helps mark the pause and the structure clearly.

Yes, that is a very good way to understand it.

Mal often gives the idea of an action happening immediately after another one. Depending on style, you can think of it as:

• as soon as
• once
• hardly/scarcely ... when
• no sooner ... than

In natural English, as soon as is usually the simplest translation. But the stronger sense of immediacy is very close to no sooner ... than.

Yes. In European Portuguese, the usual spelling is bebé.

In Brazilian Portuguese, you will usually see bebê.

They mean the same thing: baby.

So this spelling is a useful clue that the sentence is in Portuguese from Portugal.

Yes. Roncar is the standard verb meaning to snore.

Examples:

• O meu pai ronca. = My father snores.
• O bebé estava a roncar. = The baby was snoring.
• Ela não conseguiu dormir porque ele roncava muito. = She couldn’t sleep because he snored a lot.

So in this sentence, deixou de roncar is a completely normal way to say stopped snoring.