Después de la escuela, quiero volver a casa para descansar un rato.

Because después normally needs the preposition de before a noun.

• después de la escuela = after school
• después de clase = after class
• después de comer = after eating

You can use después by itself only when the rest is already understood:

• Nos vemos después. = See you later.

So in this sentence, de is required.

Spanish often uses the definite article where English does not.

So:

• después de la escuela = after school
• en la cama = in bed
• voy al trabajo = I’m going to work

This is very normal in Spanish. English often drops the article in general expressions, but Spanish often keeps it.

Also, in Spain, depending on context and age, people may more commonly say:

• el colegio for primary school
• el instituto for secondary school

So después de la escuela is understandable, but in Spain después del colegio or después del instituto may sound more natural in many situations.

Quiero is the yo form of querer.

• querer = to want
• quiero = I want

So:

• quiero volver = I want to return / I want to go back

Spanish often leaves out the subject pronoun, so yo quiero usually becomes simply quiero because the verb ending already tells you it means I want.

Because Spanish normally uses a with movement toward a destination.

• volver a casa = to go back home
• ir a casa = to go home
• llegar a casa = to arrive home

That a shows direction or destination.

So volver casa is not correct in standard Spanish.

When Spanish means home in a general sense, it usually says a casa without an article.

• Voy a casa. = I’m going home.
• Llegué a casa tarde. = I got home late.
• Quiero volver a casa. = I want to go back home.

But a la casa can be used when you mean a specific house, not just home:

• Voy a la casa de Ana. = I’m going to Ana’s house.

So here a casa means home, which is why there is no article.

It can mean both, depending on context.

• volver = to return / to go back / to come back

In this sentence, volver a casa is very naturally understood as:

• go back home
• return home

All of those are good translations. Spanish volver is very common in everyday speech.

Para is used here to express purpose or goal:

• para descansar = in order to rest / to rest

So the structure is:

• quiero volver a casa para descansar un rato
• I want to go back home to rest for a while

A very common Spanish pattern is:

• para + infinitive

Examples:

• Estudio para aprender. = I study to learn.
• Fui al supermercado para comprar pan. = I went to the supermarket to buy bread.

Because after para expressing purpose, Spanish uses the infinitive when the subject stays general or is the same as the main subject.

Here:

• quiero volver a casa = I want to go home
• para descansar un rato = to rest for a while

The person who wants to go home and the person who will rest are the same person, so the infinitive descansar is used.

No. Rato is a completely different word from rata or ratón.

• un rato = a while / a bit / some time

So:

• descansar un rato = to rest for a while

It is a very common everyday expression.

Examples:

• Espera un rato. = Wait a while.
• Voy a leer un rato. = I’m going to read for a bit.

Yes. Depending on context, descansar can mean:

• rest
• take a break
• relax

So para descansar un rato could be understood as:

• to rest for a while
• to relax for a bit
• to take a break for a while

The exact English choice depends on the situation.

It is acceptable because Después de la escuela is an introductory time phrase.

• Después de la escuela, quiero volver a casa...
• Después de la escuela quiero volver a casa...

Both can be correct. The comma helps mark a pause and can make the sentence easier to read, but in Spanish it is often omitted in short, simple sentences like this.

Yes, and in Spain that may even sound more natural in many contexts.

• Después del colegio = after school
• Después del instituto = after secondary school / after high school

Use depends on the type of school and the speaker’s age. Escuela is understandable, but in Spain people often choose a more specific word like colegio or instituto.

Because Spanish often drops subject pronouns when they are not needed.

• (Yo) quiero volver a casa.

Both are possible, but quiero alone is enough because the verb form already tells us it means I.

You would include yo only for emphasis, contrast, or clarity:

• Yo quiero volver a casa, pero él quiere salir.
• I want to go home, but he wants to go out.

Yes. Regresar and volver can both mean to return / to go back.

• Quiero volver a casa
• Quiero regresar a casa

Both are correct. In everyday speech, volver is often more common, but regresar is perfectly normal and understandable.

The sentence breaks down like this:

• Después de la escuela = time expression
• quiero = main verb, I want
• volver a casa = infinitive phrase, to go back home
• para descansar un rato = purpose phrase, to rest for a while

So the overall structure is:

After school + I want + to go home + in order to rest for a while

That is a very common Spanish pattern: time phrase + main verb + infinitive phrase + para + infinitive