Després de treballar, el pare vol parlar amb la metgessa.

Because després normally needs de before a noun or an infinitive.

So Catalan uses:

• després de treballar = after working
• després de dinar = after eating lunch
• després de la feina = after work

Without de, it would sound ungrammatical here.

After a preposition like de, Catalan uses the infinitive to express an action in a general way.

So:

• després de treballar = after working
• abans de sortir = before leaving
• sense menjar = without eating

This is similar to English using -ing in many cases, but Catalan often uses the infinitive instead.

Catalan often uses the definite article with family members and other familiar people when they are used as normal nouns in a sentence.

So el pare is very natural for the father or, depending on context, even dad/father.

Compare:

• El pare vol parlar.
• La mare arriba tard.

But if you are directly addressing him, you usually do not use the article:

• Pare, vine aquí!

Because voler is a modal-type verb, and it is followed by an infinitive.

• vol = wants
• parlar = to speak

So vol parlar literally works like wants to speak.

This same pattern appears in many Catalan sentences:

• vull menjar = I want to eat
• volen marxar = they want to leave

Only the first verb is conjugated; the second stays in the infinitive.

Parlar amb algú is a very common way to say to speak with someone or to talk to someone.

So:

• parlar amb la metgessa = speak with / talk to the doctor

You may also see parlar a algú, especially when the idea is more speaking to or addressing someone rather than having a two-way conversation. But parlar amb is extremely natural here.

Yes. Metgessa is the feminine form, so it refers to a female doctor.

• el metge = the male doctor
• la metgessa = the female doctor

Catalan nouns and articles usually show gender, so the article must agree with the noun:

• la metgessa
• el metge

The comma separates the opening time expression from the main clause:

• Després de treballar, el pare vol parlar amb la metgessa.

This is similar to English punctuation in sentences like After work, ...

In short sentences, punctuation can sometimes vary a little, but the comma is very normal and helps readability.

Yes. Catalan word order is fairly flexible.

For example, this is also possible:

• El pare vol parlar amb la metgessa després de treballar.

That version sounds natural too. The meaning is basically the same, although putting Després de treballar first gives a bit more emphasis to the time setting.

Usually, yes: the most natural reading is that the father is the one who has been working.

That is because the phrase is attached to the whole sentence and, in context, it normally connects to the subject.

Still, if a sentence like this appears without context, a small amount of ambiguity is possible. If you wanted to make it very explicit, Catalan could rephrase it, for example:

• Després que el pare hagi treballat, vol parlar amb la metgessa.
• El pare vol parlar amb la metgessa quan acaba de treballar.

But in everyday usage, the original sentence would normally be understood as after the father works.

Because la points to a specific doctor, one that the speaker and listener can identify.

• la metgessa = the doctor
• una metgessa = a doctor

So this sentence suggests that a particular doctor is meant, not just any doctor.