O Pedro mastiga pouco quando está nervoso e depois custa-lhe engolir.

In European Portuguese, it is very common to put the definite article before a person's name: o Pedro, a Maria.

It does not mean English the Pedro in a literal way. It is just a normal feature of the language. You usually leave the article out when speaking directly to the person: Pedro, anda cá.

Portuguese often leaves out subject pronouns when the subject is already clear. This is called a null-subject or pro-drop language.

Here, mastiga and está clearly refer back to Pedro, so ele is unnecessary. If you added it, it would usually sound more emphatic than neutral.

Mastigar means to chew.

Pouco here means little / not much / not enough, so mastiga pouco means he chews too little or he doesn’t chew much. In natural English, he doesn’t chew enough may sound best depending on the context.

Because pouco is being used as an adverb here, not as an adjective.

It is modifying the verb mastiga, not a noun. Adverbs do not agree in gender or number, so it stays pouco:

• Ele mastiga pouco.
• Ela mastiga pouco.

But as an adjective, it would agree:

• pouca comida
• poucos minutos

Portuguese normally uses estar for a temporary state and ser for a more permanent characteristic.

So:

• está nervoso = he is nervous right now / in that situation
• é nervoso = he is a nervous person by nature

In this sentence, the meaning is temporary, so está is the natural choice.

Because nervoso agrees with Pedro, who is masculine singular.

So the adjective must also be masculine singular:

• O Pedro está nervoso.
• A Maria está nervosa.

Here it can be understood more like when in a general, repeated sense, which in English is often close to whenever.

Because the sentence is in the present tense, it describes a habitual situation:

• Quando está nervoso... = When / Whenever he is nervous...

Depois means afterwards, later, or then.

Here it connects the two ideas in sequence:

1. Pedro chews too little when he is nervous.
2. Then swallowing becomes difficult for him.

So depois helps show the consequence of the first action.

No. Custar can mean to cost in the money sense, but it can also mean to be difficult, to take effort, or to be hard for someone.

In this sentence, it has the second meaning:

• Custa-lhe engolir = It is hard for him to swallow / He finds it hard to swallow

So this is not about price at all.

Here, lhe means to him and refers to Pedro.

With custar in this meaning, Portuguese often marks the person affected as an indirect object:

• Custa-lhe engolir = Swallowing is difficult for him
• literally, something like It is hard to him to swallow

So lhe is not him as a direct object; it is to him / for him.

This is the normal European Portuguese placement for many object pronouns in an affirmative main clause. It is called enclisis.

So:

• custa-lhe
• disse-me
• deu-lhe

In this sentence, custa-lhe is the standard European Portuguese form.

Because after custar in this structure, Portuguese uses an infinitive to name the action that is difficult.

So:

• Custa-lhe engolir = To swallow is hard for him
• more natural English: He finds it hard to swallow

The infinitive engolir works a bit like to swallow / swallowing in English.

It is still Pedro.

Even though the second part does not repeat Pedro or ele, the meaning is clear from context: Pedro is the person who has difficulty swallowing. Portuguese often leaves repeated information unstated when it is already obvious.