U petak pišu kratki test iz povijesti, pa moja kći ne želi dugo izostati.

Croatian normally uses u with the day of the week to mean on that day: u petak, u ponedjeljak, u srijedu.

So:

• u petak = on Friday

If you mean every Friday, Croatian often uses petkom instead.

Croatian very often uses the present tense for planned or scheduled future events, especially when a time expression already makes the future clear.

So:

• U petak pišu test. = On Friday they have / are writing / will write a test.

This is very natural for school schedules, appointments, timetables, and similar fixed events.

The subject is an implied they.

Croatian often leaves out subject pronouns because the verb ending already shows the person and number. The form pišu is 3rd person plural, so it already means they write / they are writing.

In this sentence, they probably means the students, the class, or the children at school.

No. In Croatian, pisati test means to take / sit / do a written test.

So students pišu test when they answer it, not when they compose it.

This is one of those places where Croatian uses write more literally than English often does.

Because test is the direct object, so it is in the accusative case. But for many masculine inanimate singular nouns, the accusative looks exactly the same as the nominative.

So:

• nominative: test
• accusative: test

That is why you see pišu kratki test, not a visibly different form of test.

Literally, iz povijesti means from history, but in this context it means in history or on history.

Croatian commonly uses:

• test iz matematike
• ispit iz biologije
• kontrolni iz kemije

So iz + genitive is a normal way to show the subject area of a test or exam.

Because after iz, Croatian uses the genitive case.

The noun is:

• nominative: povijest = history
• genitive: povijesti

So:

• iz povijesti = from/of history, idiomatically in history

Here pa means something like so, and so, or therefore.

It links the second idea as a consequence of the first:

• They have a short history test on Friday, so my daughter does not want to be absent for long.

It is very common in everyday Croatian and often sounds more natural and conversational than a more formal connector.

Because the subject changes.

In the first clause, the subject is the implied they in pišu. In the second clause, the subject is specifically moja kći.

Croatian often says the subject explicitly when:

• the subject changes,
• there could be ambiguity,
• or the speaker wants to highlight who is involved.

So moja kći makes the second clause clear.

The verb željeti is followed by an infinitive:

• želi izostati = wants to be absent / wants to miss

The word dugo is an adverb, meaning for a long time or for long. It modifies izostati.

So:

• ne želi dugo izostati = she does not want to be absent for long

This is a matter of aspect.

• izostati = perfective
• izostajati = imperfective

In this sentence, izostati suggests one whole absence or one stretch of absence:

• Ne želi dugo izostati. = She does not want to be away for long.

The imperfective izostajati is more natural for repeated or habitual absence:

• Često izostaje s nastave. = She is often absent from class.

Yes. Croatian word order is fairly flexible, because case endings and verb forms carry a lot of the grammar.

The sentence as given is neutral and natural:

• U petak pišu kratki test iz povijesti, pa moja kći ne želi dugo izostati.

But other orders are possible if you want to emphasize a different part, for example the day or the test. The original version is a good standard choice.

Yes, that is possible. But U petak pišu... sounds especially natural for a scheduled event such as a school test.

So both can work, but they do not feel exactly the same:

• U petak pišu test. = very natural for a planned school event
• U petak će pisati test. = also correct, but a little more plainly future

In everyday Croatian, the present tense is often preferred in this kind of context.