Learn Russian: Кто прожёг сестре платье и оторвал ей карман? - Who burned a hole in my sister's dress and tore off her pocket?

This is the dative of detriment. When an action negatively affects someone's body or closely held personal items like clothing, Russian prefers to put the affected person in the dative case (сестре, ей) rather than using a genitive possessive. It emphasizes that the damage happened to her, not just to her property.

Why are the verbs прожёг and оторвал in the masculine singular form when the victim is female?

The verbs must agree with the grammatical subject of the sentence, which is Кто (Who). In Russian, the pronoun кто always takes masculine singular agreement in the past tense, regardless of the actual gender of the person who committed the action or the gender of the victim.

What does the prefix про- add to the verb жечь (to burn) in прожёг?

The prefix про- often indicates an action that goes completely through an object. While жечь means to burn in general, прожечь specifically means to burn a hole through something, which fits perfectly with ruining a dress.

Could I use порвал instead of оторвал for tearing the pocket?