Can someone explain to me why these answers are incorrect? then explain the correct the answer?

Question 2. I write a letter to my brother.

Translation: Yo escribo una carta a mi hermano.

Yo se la escribo.

Explanation: Transitive verbs need a direct object to complete their meaning. The direct object of the verb to write is "una carta", this is a feminine and singular noun, so the direct object pronoun is "la" that matches gender and number with the object it replaces. The indirect object is "mi hermano", which is a singular noun and the indirect object pronoun is "le" because it has to match in number with the object it replaces. When the direct object and indirect object pronouns appear in the same sentence, the indirect object pronoun is always written first and replaced with "se", so in this sentence it is "se la"

Question 4. You buy a gift for your mom.

Translation: Tú compras un regalo para tu mamá.

Tú se lo compras.

Explanation: Transitive verbs need a direct object to complete their meaning. The direct object of the verb to buy is "un regalo", this is a masculine and singular noun, so the direct object pronoun is "lo" that  matches gender and number with the object it replaces. The indirect object is "tu mamá", which is a singular noun and the indirect object pronoun is "le" because it has to match in number with the object it replaces. When the direct object and indirect object pronouns appear in the same sentence, the indirect object pronoun is always written first and replaced with "se", so in this sentence it is "se lo"

this question is given using the conditional form. conditional tenses are is used when talking about hypothetical situations and probabilities. also, this is used when making polite requests. so comprarías is the conjugation of the verb comprar that matches the second person singular in the conditional. finally:

¿cuál comprarías tú?