Després de dinar, he de parlar amb una veïna de la ciutat.

Both are possible, but they are not exactly the same.

• després de dinar = after having lunch / after lunch in a general sense
• després del dinar = after the lunch / after that lunch meal, referring to a specific meal as a noun

In your sentence, després de dinar uses the infinitive dinar and is the most natural way to say after eating lunch.

Here, it is functioning as a verb infinitive.

After the preposition de, Catalan often uses an infinitive:

• abans de sortir = before leaving
• després de dinar = after having lunch

That said, dinar can also be a noun meaning lunch. So English may translate this very naturally as after lunch, even though Catalan is using a verb form here.

It is the structure haver de + infinitive, which expresses obligation or necessity.

So:

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

Together:

• he de parlar = I have to talk

This is a very common Catalan way to say have to.

Yes, it uses the same verb, haver, but the construction is different.

• he parlat = present perfect, I have spoken
• he de parlar = obligation, I have to speak

The key difference is:

• he + participle → perfect tense
• he de + infinitive → obligation

So the little word de changes the structure completely.

Because Catalan often drops subject pronouns when the verb already makes the subject clear.

• he de parlar already shows I because he is first person singular.
• Jo he de parlar is possible, but it adds emphasis, contrast, or clarification.

Catalan is a pro-drop language, like Spanish or Italian, so omitting jo is normal.

Yes, they both mean I have to.

• he de parlar
• haig de parlar

Both are correct. The difference is mostly one of usage and register:

• he de is standard and common in writing
• haig de is also very common, especially in speech in many areas

So a learner should recognize both.

Because these prepositions mean different things.

• parlar amb algú = to speak with/to someone
• parlar de alguna cosa = to speak about something

In this sentence:

• parlar amb una veïna = talk with a neighbour

If it said parlar de la ciutat, that would mean talk about the city, which is different.

Yes. veïna is the feminine singular form, so it refers to a woman.

Compare:

• un veí = a male neighbour
• una veïna = a female neighbour

So the sentence specifically tells you the neighbour is female.

The diaeresis on ï shows that the i is pronounced separately, not merged into the previous vowel.

So veïna is pronounced in three syllables:

• ve-ï-na

Without the diaeresis, a learner might wrongly try to read ei as one sound. The mark tells you to keep them separate.

It modifies veïna.

So the structure is:

• parlar amb
  • una veïna de la ciutat

That means:

• a neighbour from the city
• or a neighbour who belongs to the city / lives in the city, depending on context

It does not go with parlar. If the city were the topic of conversation, Catalan would normally say parlar de la ciutat.

Because Catalan only contracts de + el into del.

So:

• de + el → del
• de + la stays de la

Since ciutat is feminine:

• la ciutat
• de la ciutat

So del ciutat would be incorrect.

Because Després de dinar is an introductory time expression placed at the beginning of the sentence.

The comma helps separate that opening phrase from the main clause:

• Després de dinar, he de parlar...

This is very natural in writing. In shorter sentences, some writers may omit such commas, but here the comma is clear and standard.