1. In Spanish, when you have to objects (a direct and an indirect one, as is the case here), you will first place the indirect object (= para mi), and then the direct object (= un regalo). The pronoun ME refers to para mi, and the pronoun LO refers to un regalo. Thus, the correct answer is Me lo trajo.
2. The same thing goes for the second sentence. There are two objects here as well: la carta is direct object, a mi is the indirect object. You place the indirect object first when you are using pronouns - ME refers to a mi, and LA refers to la carta. Thus, the correct answer is Me la dio.
