Post scholam discipuli domi prandium breve sumunt.

Because post is a preposition that takes the accusative. So post scholam means after school.

This is a general rule:

• post + accusative = after ...

So:

• schola = school
• scholam = accusative singular, used here because of post

Discipuli is nominative plural, and it is the subject of the sentence.

It means the students or simply students, depending on context.

So the basic structure is:

• discipuli = the students
• sumunt = eat / have / take

Together: the students eat/have

Because domi is a special locative form meaning at home.

Latin sometimes uses special forms instead of a preposition for certain places, especially with words like domus.

So:

• domi = at home
• domum = to home / homeward
• domo = from home

This is one of those forms learners simply get used to seeing.

It is accusative singular, because it is the direct object of sumunt.

The students are doing the action of sumunt to prandium breve:

• they eat/have a short lunch

So:

• prandium = lunch, midday meal
• prandium breve = a short lunch

Because prandium is neuter.

The adjective has to agree with the noun in:

• gender
• number
• case

Since prandium is neuter accusative singular, the adjective is also neuter accusative singular:

• prandium breve

For many Latin adjectives, the neuter nominative singular and neuter accusative singular look the same. That is why you get breve, not brevem.

Sumunt is from sumere, which literally often means to take. But with food or meals, it can mean to take, to eat, or to have.

So in this sentence:

• prandium sumere = to have/eat lunch

Sumunt is:

• present tense
• active
• indicative
• 3rd person plural

So it means they have/eat.

Because Latin does not have articles like English the and a/an.

So a noun like discipuli can mean:

• students
• the students

And prandium breve can mean:

• a short lunch
• the short lunch

The exact English wording depends on context.

Latin word order is much more flexible than English word order because the endings show the grammatical roles.

This sentence is arranged as:

• Post scholam = after school
• discipuli = the students
• domi = at home
• prandium breve = a short lunch
• sumunt = have/eat

A very literal order would be:

• After school the students at home a short lunch eat.

That sounds odd in English, but it is normal in Latin. Latin often puts the verb at the end, and it can move phrases around for emphasis or style.

In a sentence like this, it normally means after school in the sense of after the school day / after classes.

Even though schola can mean school, the phrase post scholam is naturally understood as a time expression here.

So the meaning is not usually:

• physically behind the school building

It is usually:

• after school is over

It can be either in principle, but in a sentence like this it most naturally describes a habitual action:

• After school, the students eat/have a short lunch at home.

Latin present tense often covers both:

• they are eating
• they eat
• they usually eat

The wider context tells you which is intended. Here, the sentence sounds like a regular routine.

Yes. Latin allows a lot of variation in word order.

For example, these would still be understandable:

• Discipuli post scholam domi prandium breve sumunt.
• Post scholam domi discipuli prandium breve sumunt.

The core meaning stays the same because the endings show the function of each word. The main differences would be style, focus, or emphasis, not basic meaning.