Learn Hardcore Latin: Frater vinum patri petit. - The brother asks father for wine.

Vinum is in the accusative case (direct object case), meaning it is what is being sought. If it were vini, it would be genitive (of the wine), and vino would be dative or ablative (to the wine / by or with the wine). Here, vinum directly receives the action of petit (he seeks).

Why is patri in the sentence, and why is it in the dative case?

Patri indicates the recipient or beneficiary of the action, which is why it is in the dative rather than some other case. The brother is seeking wine for the father, so patri (to/for the father) makes sense in Latin.

How come petit is the correct form of the verb? Could we say petunt or petit?

Since the subject — frater (brother) — is singular (he), the verb must agree with a third-person singular subject. In the present tense, the form is petit. Petunt would be the third-person plural (they seek).

Is it acceptable to change the word order to Frater patri vinum petit?

Yes! Latin word order is quite flexible because the case endings signal grammatical functions. Frater patri vinum petit conveys the same meaning. However, emphasis and style might shift slightly, but grammatically it remains correct.

Why does frater end in -er and not something like -us?

Frater is a third-declension noun (though many students first encounter typical second-declension nouns ending in -us). This is just its nominative singular form. Other cases change stem endings accordingly, e.g., fratris (genitive singular), fratrem (accusative singular), etc.