Primer he de parlar amb la professora, i després puc tornar a casa.

Here primer works like an adverb or sequence marker: first, first of all.

Catalan often uses primer ... després ... to organize actions in order:

• primer = first
• després = afterwards / then

So the sentence is structured as:

• Primer: the first thing that must happen
• després: the next thing that can happen

In this use, primer does not change to agree with another word.

He de parlar is the structure haver de + infinitive, which means to have to, to need to, or sometimes must.

Breakdown:

• he = I have (from the verb haver)
• de parlar = to speak / to talk

So:

• he de parlar = I have to talk / I need to speak

A very important point for English speakers: Catalan he has nothing to do with English he.

Yes. Haver de + infinitive is a very standard and common Catalan way to express obligation or necessity.

So:

• he de parlar = I have to speak
• has de parlar = you have to speak
• ha de parlar = he/she has to speak

It can sound like:

• have to
• need to
• sometimes must

depending on context.

Parlar amb usually means to talk with / speak with, suggesting some kind of interaction or conversation.

Parlar a can mean to speak to someone, often with more emphasis on addressing that person rather than having a two-way conversation.

So in this sentence, parlar amb la professora is very natural if the idea is I need to talk with the teacher.

Because Catalan normally uses the definite article with a specific person or role.

Here la professora means the teacher, referring to a particular teacher. The article is not optional in normal Catalan.

Also:

• professora is feminine
• so the article is la

Compare:

• el professor = the male teacher
• la professora = the female teacher

Puc comes from the verb poder, which means can / to be able to.

So:

• puc = I can
• pots = you can
• pot = he/she can

It is an irregular verb, so the form puc does not look very much like the infinitive poder.

In this sentence:

• puc tornar a casa = I can go back home

Here tornar means to return or to go back, and a casa means home.

So:

• tornar a casa = to go back home / to return home

This is a very common expression in Catalan.

Yes. Tornar a + infinitive can mean to do something again.

For example:

• tornar a parlar = to speak again
• tornar a llegir = to read again

But that is not what is happening in your sentence.

In tornar a casa, a casa is a place, not an infinitive. So the meaning is:

• return home

not

• do something again

When casa means home, Catalan usually does not use the article in common expressions.

Very common patterns:

• ser a casa = to be at home
• anar a casa = to go home
• tornar a casa = to return home

If you say la casa, you are usually talking about the house as a building, not home in the everyday sense.

In your sentence, després means afterwards / then.

So:

• Primer he de parlar amb la professora, i després puc tornar a casa.
• First I have to talk to the teacher, and then I can go home.

But després de means after followed by a noun or another element:

• després de classe = after class
• després de dinar = after lunch / after eating lunch

So:

• després = afterwards / then
• després de ... = after ...

Usually, no.

In Catalan, a comma before i (and) is often omitted in a simple sentence like this. Many people would write:

Primer he de parlar amb la professora i després puc tornar a casa.

The comma in your version is understandable as a pause or stylistic choice, but in basic coordination it is often left out.

Yes, to some extent.

Catalan has some flexibility, especially with sequence markers like primer and després. For example, these are also possible:

• Primer he de parlar amb la professora; després puc tornar a casa.
• He de parlar amb la professora primer, i després puc tornar a casa.

The original version sounds natural because primer and després clearly show the order of events.

It tells you where the stress goes: des-PRÉS.

Catalan written accents often help with pronunciation by showing the stressed syllable. So in després, the last syllable is stressed.

That makes it easier to distinguish the natural rhythm of the word when speaking.