Answer: 1) carefully and efficiently, and 2) plays bass and sings backup for his band.
Explanation: parallelism or parallel structure is a literary device that consists in the repetition of the grammatical structure of different words or phrases in a sentence or paragraph, in order to emphasize an idea or to create an impact in the audience. In the first sentence, the option that gives parallel structure is the first one: Vicky does her homework carefully and efficiently (they are both adverbs). In the second sentence the correct answer is the second one: Derek plays bass and sings backup for his band ("plays" and "sings" are in the same tense).