Después de un suspiro, mi madre siguió hablando con calma.

Because después de is the normal way to say after when it is followed by a noun or noun phrase:

• después de un suspiro = after a sigh
• después de la cena = after dinner

If what follows is a conjugated verb clause, Spanish often uses después de que:

• Después de que llegó, hablamos. = After he arrived, we talked.

So in this sentence, un suspiro is a noun phrase, which is why de is enough.

Because the sentence is referring to the action as a thing: a sigh.

• suspiro = sigh (noun)
• suspirar = to sigh (verb)

So:

• Después de un suspiro = After a sigh
• Después de suspirar would mean After sighing

Both are possible in Spanish, but they are structured differently.

Seguir + gerund is a very common Spanish structure meaning to keep doing something or to continue doing something.

So:

• siguió hablando = she continued speaking / she went on talking

Other examples:

• Siguió caminando. = He kept walking.
• Seguimos estudiando. = We continued studying.

This is one of the most useful patterns to learn in Spanish.

Because after seguir in this meaning, Spanish normally uses a gerund:

• seguir hablando
• seguir comiendo
• seguir trabajando

This works like keep/continue + -ing in English.

So:

• siguió hablando = continued speaking
• not normally siguió hablar

Siguió is preterite, which presents the action as a completed event in the story sequence.

In this sentence, the idea is something like:

1. there was a sigh,
2. then the mother continued speaking.

That makes siguió sound like the next step in the narrative.

If you said seguía hablando, it would usually describe an ongoing background situation:

• Mi madre seguía hablando cuando entré. = My mother was still talking when I came in.

So here, siguió fits the sense of then she went on speaking.

Yes. Continuó hablando is grammatically correct and means almost the same thing.

But seguir + gerund is very natural and very common in everyday Spanish:

• Mi madre siguió hablando con calma.
• Mi madre continuó hablando con calma.

The version with siguió often feels slightly more idiomatic in ordinary speech.

Literally, con calma means with calm. In natural English, that usually becomes:

• calmly
• in a calm way
• with composure

Spanish often uses con + noun where English might prefer an adverb.

Compare:

• con cuidado = carefully
• con paciencia = patiently
• con calma = calmly

So habló con calma is a very natural Spanish way to express a calm manner of speaking.

As the subject, mi madre is the normal choice if you want to mean my mother clearly.

Just madre by itself would usually not work well here as a standalone subject in normal modern Spanish. You would generally need:

• mi madre = my mother
• la madre = the mother
• mamá = mum/mom

Spanish sometimes omits possessives with family/body parts in other structures, but here mi madre is the straightforward form.

It separates the introductory phrase from the main clause:

• Después de un suspiro, / mi madre siguió hablando con calma.

This comma helps the rhythm and makes the pause clearer.

In Spanish, commas after short introductory phrases can sometimes be optional, but here it is very natural and stylistically neat. Without the comma, the sentence would still be understandable:

• Después de un suspiro mi madre siguió hablando con calma.

But the version with the comma reads more smoothly.

Yes, Spanish word order is fairly flexible, though some versions sound more natural than others.

Possible alternatives include:

• Mi madre siguió hablando con calma después de un suspiro.
• Con calma, mi madre siguió hablando después de un suspiro.

The original version puts Después de un suspiro first, which highlights the sequence of events. It creates a nice narrative flow: first the sigh, then the continued speaking.

The written accents show where the stress goes:

• después → stress on the second syllable: des-PUÉS
• siguió → stress on the last syllable: si-GUIÓ

That accent in siguió is especially useful because it tells you the ending is stressed.

Also, in siguió, the u in gui is silent:

• siguió sounds roughly like see-GYOH

So it is not pronounced see-goo-ee-O.