Mi abuelo se quedó dormido en el sofá después de cenar.

Because se quedó dormido means fell asleep, while durmió means slept.

So:

• Mi abuelo se quedó dormido = my grandfather fell asleep
• Mi abuelo durmió = my grandfather slept

The Spanish sentence focuses on the moment or change of state: he was awake, and then he fell asleep.

Quedarse dormido is a very common expression meaning to fall asleep.

Literally, quedarse often means to remain / to stay, but in expressions like this it often means to end up becoming a certain way.

So:

• quedarse dormido = to fall asleep
• quedarse callado = to go quiet / fall silent
• quedarse solo = to end up alone

In this sentence, se quedó dormido describes the result: he ended up asleep.

The verb here is quedarse, not just quedar.

These are different:

• quedar can mean things like to remain, to meet, or to be left
• quedarse often means to stay, to keep, or in some expressions to end up becoming

So se is part of the verb quedarse. It is not optional here.

Examples:

• Me quedé en casa = I stayed at home
• Se quedó dormido = he fell asleep

Quedó is the preterite, which is used for a completed event. That fits well with falling asleep, because it happened as a single event in the story.

• se quedó dormido = he fell asleep

If you used se quedaba dormido, that would usually suggest a repeated action, a habitual action, or background description:

• Después de cenar, se quedaba dormido en el sofá = After dinner, he would fall asleep on the sofa

So in your sentence, the preterite is used because it refers to one completed event.

Because dormido agrees with abuelo, which is masculine singular.

• abuelo = masculine singular
• so: dormido

If the subject were feminine, it would change:

• Mi abuela se quedó dormida = My grandmother fell asleep

If it were plural:

• Mis abuelos se quedaron dormidos
• Mis abuelas se quedaron dormidas

It behaves like an adjective describing the result of the action.

In se quedó dormido:

• se quedó = he ended up / he became
• dormido = asleep

So the whole expression means he became asleep → he fell asleep.

That is why dormido changes for gender and number:

• dormido
• dormida
• dormidos
• dormidas

In Spanish, it is very normal to use the definite article in places where English often does not.

So Spanish says:

• en el sofá = on the sofa

Even if English might sometimes say on the couch or just on a sofa depending on context, Spanish naturally uses el here.

Also note that sofá is masculine:

• el sofá

After después de, Spanish often uses an infinitive when the subject is the same and the action is general.

So:

• después de cenar = after having dinner / after dinner

The structure is:

• después de + infinitive

Examples:

• después de comer = after eating
• después de trabajar = after working
• después de cenar = after having dinner

Después cenar is incorrect because you need the de.

Después de cena is also not the normal structure here. If you want a noun, you would usually say después de la cena = after dinner / after the meal.

Yes, absolutely. That is also correct and natural.

• se durmió = fell asleep
• se quedó dormido = fell asleep

Both work, but there can be a small nuance:

• dormirse is the straightforward verb to fall asleep
• quedarse dormido can sometimes suggest drifting off, nodding off, or ending up asleep, often a bit unintentionally

In many everyday situations, they are very close in meaning.

Usually, abuelo means grandfather. In this sentence, Mi abuelo clearly means my grandfather.

In some contexts, people may use abuelo more loosely for an elderly man, but that is not the normal meaning unless the context makes it clear.

So here, the natural reading is definitely my grandfather.

Yes, Spanish word order is flexible, but the version you have is very natural:

• Mi abuelo se quedó dormido en el sofá después de cenar.

This gives the information in a clear order:

1. who: Mi abuelo
2. what happened: se quedó dormido
3. where: en el sofá
4. when/after what: después de cenar

You could also hear:

• Después de cenar, mi abuelo se quedó dormido en el sofá.

That version puts more emphasis on after dinner.

Both are correct.

A typical Spain pronunciation would be roughly:

Mi a-BWE-lo se ke-DO dor-MI-do en el so-FA des-PWES de ce-NAR

A few useful pronunciation notes:

• abuelo has stress on bue
• quedó has stress on the last syllable because of the accent mark
• sofá also has final stress because of the accent mark
• in much of Spain, c before e in cenar sounds like the th in thin

So in most of Spain:

• cenar sounds like the-NAR

But in Latin America, it would usually sound like:

• se-NAR

Both are correct in their own varieties.