Después de cenar, nos sentamos en un banco del paseo y miramos el mar.

After a preposition such as de, Spanish normally uses the infinitive when the subject stays the same.

So:

• después de cenar = after having dinner / after dinner
• literally, it is after to dine, but in natural English we say after dinner or after eating dinner

If you use a fully conjugated verb, Spanish usually needs a different structure, for example:

• después de que cenamos = after we had dinner

In your sentence, después de cenar is the most natural and compact way to say it.

Because Después de cenar is an introductory time phrase.

Spanish often puts a comma after this kind of opening element:

• Después de cenar, ...
• Al día siguiente, ...
• Por la noche, ...

It helps separate the time setting from the main action. In some short phrases, punctuation can vary, but the comma here is very normal and clear.

Nos sentamos comes from the verb sentarse, which means to sit down.

• sentar = to seat someone / to sit someone down
• sentarse = to sit down

So:

• nos sentamos = we sat down

The nos is the reflexive pronoun for we. It does not usually get translated literally into English, but it is required in Spanish with sentarse.

Compare:

• Sentamos al niño. = We sat the child down.
• Nos sentamos. = We sat down.

Without nos, the meaning changes.

Good question: it really can be both, depending on context.

For many -ar verbs, the first-person plural form is the same in the:

• present: nos sentamos = we sit down / we sit
• preterite: nos sentamos = we sat down

The same happens with miramos:

• miramos = we look
• miramos = we looked

So how do you know? Context.

Here, the sentence is telling a past sequence of events:

• Después de cenar
• nos sentamos
• miramos

That makes the past reading the natural one.

Because the sentence presents the actions as completed events in a sequence.

The preterite is used for actions that move the story forward:

• nos sentamos = we sat down
• miramos = we looked at

If the speaker wanted a more descriptive or habitual background feeling, the imperfect would be more likely:

• nos sentábamos
• mirábamos

That would suggest something like:

• we used to sit down...
• we were sitting...
• we used to look at the sea...

So the preterite here gives a clear, finished chain of actions.

In Spanish, en is very commonly used where English uses on, in, or at, depending on the context.

So:

• en un banco = on a bench

Using sobre would sound more like on top of in a physical, literal sense. For normal sitting, en un banco is the natural choice.

This is one of those places where Spanish and English divide space differently.

Here banco means bench, not bank in the money sense.

Spanish banco can mean different things depending on context, including:

• bank (financial institution)
• bench
• sometimes other extended meanings

Because the sentence says nos sentamos en un banco, it clearly means a bench.

Here paseo most likely means a promenade, seafront walk, or place for strolling.

In Spain, paseo often refers to:

• a pleasant public walkway
• an avenue for walking
• a promenade near the sea

So un banco del paseo suggests a bench located along that promenade or walkway.

It does not have to mean the action of walking here; it is being used as a place noun.

Because de + el contracts to del in Spanish.

So:

• de + el = del
• a + el = al

That is why you get:

• un banco del paseo = a bench of/from/on the promenade

But this only happens with el, not with other articles:

• de la playa → not contracted
• de los jardines → not contracted
• de las calles → not contracted

Because el mar is the direct object of mirar, and it does not take the personal a.

Spanish uses the personal a mainly with specific people (and sometimes pets or personified beings):

• Miramos a Ana.
• Miramos al perro. (possible, especially if treated as an individual being)

But with a thing like el mar, you just say:

• miramos el mar

So:

• mirar el mar = correct
• mirar al mar = not the normal structure for this meaning

Because in Spanish, nouns often need an article where English would not use one.

So Spanish says:

• miramos el mar
• escuchamos la música
• abrimos la puerta

English often drops the article in some expressions, but Spanish usually keeps it.

Here el mar refers to the sea visible in the scene, and the article sounds completely natural. Saying miramos mar would be ungrammatical.

Because mirar means to look at, while ver means to see.

• mirar = direct your eyes toward something
• ver = perceive something visually

In this sentence, the idea is active and intentional: they sat down and looked at the sea.

So:

• miramos el mar = we looked at the sea

If you used vimos el mar, it would mean we saw the sea, which is possible in other contexts, but it gives a different nuance.

Yes. Spanish has several possible ways to express this idea, though they are not all identical in style or emphasis.

For example:

• Después de cenar, ... = very natural
• Tras cenar, ... = a bit more formal/literary
• Después de la cena, ... = after dinner, using a noun
• Cuando terminamos de cenar, ... = when we finished dinner

In your sentence, Después de cenar is simple, idiomatic, and very common.