Djeca imaju pravo na kratak odmor poslije škole.

Djeca is the nominative plural form of dijete (child) and it functions as the subject of the sentence.

• djeca = children (as the doer/subject)
• djece is usually genitive (of children / some children)
• djeci is usually dative/locative (to children / about children)
  This is also an irregular pair: dijete → djeca (not a regular plural like dijeti).

Because the subject djeca is plural, the verb must be 3rd person plural:

• ja imam (I have)
• ti imaš (you have)
• on/ona/ono ima (he/she/it has)
• mi imamo (we have)
• vi imate (you plural have)
• oni/one/ona imaju (they have)

It’s a fixed and very common construction meaning to have the right to.
Grammatically:

• pravo is the object of imati (to have)
• na + accusative expresses what that right is directed toward (right to something)

So imaju pravo na ... is best learned as a chunk: imati pravo na + (acc.)

Here na requires the accusative because it expresses a goal/entitlement (right to something).
So kratak odmor is in the accusative.

Note: na can also take locative in other meanings (often location), but not in this construction.

Because odmor is masculine singular inanimate, and in Croatian the accusative for masculine inanimate nouns is the same as the nominative.

• Nominative: kratak odmor
• Accusative (inanimate): kratak odmor (same form)

Kratki would be used in other cases/contexts (for example masculine nominative plural: kratki odmori).

A quick practical way:

• Many nouns ending in a consonant (like odmor) are masculine.
• Inanimate means it’s not a person/animal (so it doesn’t behave like animate nouns in the accusative).

That matters because masculine animate nouns change in the accusative (e.g., vidim dobrog psa), while odmor doesn’t.

Poslije requires the genitive.
So škole is genitive singular of škola.

• Nominative: škola
• Genitive: škole
  Therefore: poslije škole = after school

Often, yes. Both commonly mean after and take the genitive:

• poslije škole
• nakon škole

Typical nuance: nakon can sound a bit more neutral/formal in some contexts, while poslije is very everyday/common, but in this sentence both are natural.

Yes, Croatian word order is relatively flexible because cases show roles. The most neutral is what you have:

• Djeca imaju pravo na kratak odmor poslije škole.

But you could emphasize time by moving it forward:

• Poslije škole djeca imaju pravo na kratak odmor.

Both are grammatical; the difference is mainly emphasis and style.