Después de cenar, mi hermana se pone a revisar la lista de cosas que faltan para mudarse.

Both are possible, but they mean slightly different things.

• después de cenar = after having dinner / after eating dinner
  • This is después de + infinitive, which is a very common Spanish structure.
• después de la cena = after dinner / after the dinner meal

Spanish often uses después de + infinitive where English might use either after + -ing or after + noun.

Examples:

• Después de comer, salimos. = After eating / After lunch, we went out.
• Después del trabajo, vuelvo a casa. = After work, I go home.

So después de cenar focuses more on the action of eating dinner.

Ponerse a + infinitive means to start doing something, often with the idea of suddenly getting going or setting oneself to a task.

So:

• se pone a revisar = she starts checking/reviewing

It does not literally mean she puts herself to review in normal English. It is an idiomatic verbal structure.

Similar examples:

• Me puse a leer. = I started reading.
• Se puso a llorar. = He/She started crying.
• Nos pusimos a trabajar. = We started working.

In this sentence, it suggests that after dinner, the sister begins the task of checking the list.

Because the verb here is ponerse, not just poner.

• poner usually means to put
• ponerse a + infinitive is a fixed expression meaning to start doing something

So in this sentence:

• mi hermana se pone a revisar...

the se is part of the pronominal verb ponerse.

Compare:

• Pone el libro en la mesa. = She puts the book on the table.
• Se pone a leer el libro. = She starts reading the book.

So the se is not optional here.

Because the pattern is:

ponerse a + infinitive

This is just the structure the verb uses when it means to begin doing something.

Examples:

• Se pone a estudiar. = She starts studying.
• Me pongo a cocinar. = I start cooking.
• Se pusieron a hablar. = They started talking.

You should learn ponerse a as a complete expression.

Because the subject of faltan is cosas, which is plural.

The relevant part is:

• la lista de cosas que faltan

Literally:

• the list of things that are missing / still needed

Here, que faltan describes cosas:

• cosas = things
• faltan = are missing / are still needed

Since cosas is plural, the verb must also be plural:

• la cosa que falta = the thing that is missing
• las cosas que faltan = the things that are missing

This is a very common point of confusion because in English we often say what’s missing without clearly showing agreement.

Que faltan is a relative clause describing cosas.

Break it down:

• la lista = the list
• de cosas = of things
• que faltan = that are missing / that are still needed

So the full idea is:

• the list of things that are still missing
• or the list of things still needed

In Spanish, que often means that / which / who in this kind of clause.

Examples:

• el libro que leo = the book that I’m reading
• las personas que viven aquí = the people who live here
• las cosas que faltan = the things that are missing

Because the verb for to move house / to move to another home is usually mudarse, which is reflexive.

• mudarse = to move house / to move to a new place
• mudar by itself usually means to change something, and it is much less common in this everyday sense

So:

• para mudarse = in order to move

Examples:

• Nos vamos a mudar. = We’re going to move.
• Quiere mudarse a Madrid. = He/She wants to move to Madrid.

A useful contrast:

• mudar algo = to change something
• mudarse = to move oneself / move house

The most natural reading is that it refers to mi hermana, yes.

The sentence suggests:

• After dinner, my sister starts checking the list of things that are still needed for moving.

Because the main subject is mi hermana, listeners will usually assume she is the one moving, unless the wider context says otherwise.

That said, Spanish can sometimes leave this a little more open than English. Depending on context, it could also mean she is reviewing a list connected with someone’s move or a household move.

But in isolation, the default interpretation is:

• my sister is the one preparing to move

Here revisar means to check, to go over, or to review.

In this sentence:

• revisar la lista = to check/go over the list

Be careful with the English cognate revise:

• In British English, revise often means study again before an exam
• Spanish revisar usually means inspect, check, look over, or review

Examples:

• Voy a revisar el documento. = I’m going to check/review the document.
• El técnico revisó el coche. = The mechanic checked the car.

So here it means she is looking through the list to see what is still missing.

Yes. Both are possible, but they have slightly different tones.

• empieza a revisar = she begins to review/check
  • more neutral
• se pone a revisar = she starts checking
  • often feels a little more vivid, dynamic, or immediate

Compare:

• Después de cenar, mi hermana empieza a revisar la lista...
• Después de cenar, mi hermana se pone a revisar la lista...

Both are correct.
Se pone a can sometimes suggest that she gets down to the task at that moment.

That opening phrase sets the time: after dinner.

Spanish often puts a time expression at the beginning of the sentence, just like English can:

• Después de cenar, mi hermana...
• After dinner, my sister...

This is very natural word order. It helps frame the action before introducing what happens.

You could also say:

• Mi hermana se pone a revisar la lista... después de cenar.

But the original version sounds smoother and more natural in most contexts.

A useful breakdown is:

• Después de cenar, = After dinner / After having dinner,
• mi hermana = my sister
• se pone a revisar = starts checking / starts going over
• la lista de cosas = the list of things
• que faltan = that are missing / still needed
• para mudarse = in order to move / for moving house

This kind of chunking is helpful because the sentence contains several common Spanish patterns:

• después de + infinitive
• ponerse a + infinitive
• noun + que + verb
• para + infinitive