Después de comer, limpio el fregadero y paso la aspiradora por la cocina.

Because after a preposition like de, Spanish normally uses the infinitive when the subject stays the same.

So:

• después de comer = after eating / after I eat

You do not use the conjugated form como here.

Compare:

• Después de comer, limpio el fregadero.
• Antes de salir, cierro la puerta.
• Después de estudiar, descanso.

This is very common in Spanish:

• antes de + infinitive
• después de + infinitive

Spanish often leaves out subject pronouns because the verb ending already shows who is doing the action.

• limpio = I clean
• paso = I pass / I run / I vacuum

So yo is not necessary unless you want emphasis or contrast.

For example:

• Después de comer, limpio el fregadero. = normal
• Yo limpio el fregadero, no tú. = emphatic

Omitting the pronoun is one of the most common features of Spanish.

The present tense in Spanish is often used to talk about:

• habits
• routines
• things you usually do

So this sentence sounds like part of a routine:

• Después de comer, limpio el fregadero y paso la aspiradora por la cocina.

It means something like:

• After eating, I clean the sink and vacuum the kitchen.
• or After meals, I clean the sink and vacuum the kitchen, depending on context

Spanish uses the simple present here just like English often does for habits.

In Spain, el fregadero usually means the kitchen sink.

It comes from the verb fregar, which means to scrub / to wash up.

So:

• fregar los platos = to wash the dishes
• el fregadero = the sink

A learner may confuse it with other words like:

• lavabo = sink/washbasin, usually in the bathroom
• pila = sink in some regions, but less standard for Spain in this context

In this sentence, el fregadero is definitely the kitchen sink.

Spanish uses the definite article very naturally with household objects and places, especially when the object is specific or understood from context.

So:

• limpio el fregadero
• paso la aspiradora
• barro la cocina
• cierro la puerta

This is very normal Spanish. Even when English might be less explicit, Spanish often keeps the article.

Because in Spanish, the most common way to say to vacuum is the expression:

• pasar la aspiradora

Literally, this is something like to pass the vacuum cleaner, but you should think of it as a fixed phrase meaning:

• to vacuum

So:

• Paso la aspiradora por la cocina. = I vacuum the kitchen.

You may also hear:

• aspirar = to suck up / to vacuum, but it is less common in everyday speech for this household action
• pasar el aspirador in some regions, but pasar la aspiradora is very standard in Spain

Both can be possible in some contexts, but por la cocina gives the idea of moving the vacuum around/through the kitchen area.

• pasar la aspiradora por la cocina = to vacuum around the kitchen / vacuum the kitchen area
• pasar la aspiradora en la cocina = to use the vacuum in the kitchen

With pasar la aspiradora, por is very common because it suggests movement across a surface or area.

Similar patterns:

• pasar el trapo por la mesa = wipe the cloth over the table
• pasar la escoba por el suelo = sweep over the floor

So por fits the physical action very well.

Here it means the kitchen as a room.

In Spanish, la cocina can mean:

1. the kitchen = the room
2. the stove/cooker in some contexts

But in this sentence, because of paso la aspiradora por la cocina, it clearly means the room, not the appliance.

Because Después de comer is an introductory time expression.

Spanish often uses a comma after an introductory phrase like this, especially when it comes at the beginning of the sentence:

• Después de comer, limpio el fregadero...
• Por la mañana, salgo a correr.
• Al llegar a casa, me ducho.

The comma helps separate the time setting from the main action.

Yes. Tras comer is correct and means basically the same thing:

• Tras comer, limpio el fregadero...

But there is a slight difference in feel:

• después de comer = more common and neutral
• tras comer = a bit more concise, sometimes slightly more formal or written

For most learners, después de comer is the safest and most natural option in everyday speech.

Yes, but the meaning is a little different in nuance.

• después de comer = after eating
• después de la comida = after the meal / after lunch

The first focuses more on the action of eating.
The second refers more to the meal as an event or thing.

In many situations they are very close, but después de comer is especially natural for everyday routines.

It can cover either idea depending on context.

• limpiar is a broad verb meaning to clean
• In a kitchen routine, limpio el fregadero often suggests I clean/wipe out the sink

If you want to be more specific, Spanish can say:

• friego el fregadero = I scrub the sink
• limpio el fregadero con una bayeta = I clean the sink with a cloth

But limpio el fregadero is perfectly natural and general.

Yes, the Spanish suggests a sequence of routine actions:

1. Después de comer = after eating
2. limpio el fregadero
3. y paso la aspiradora por la cocina

So the sense is:

• After eating, I clean the sink and then vacuum the kitchen.

Spanish does not need a separate word for then here, because the order is already clear from the structure. If you wanted to make it extra explicit, you could say:

• Después de comer, limpio el fregadero y luego paso la aspiradora por la cocina.

Here luego = then / afterwards.