Here are the answers to your questions:
Question 1: "Like a beacon in the darkest night, her words illuminated the path forward for the civil rights movement."
Answer: c. Simile
(The phrase "like a beacon" makes a comparison using "like," which is characteristic of similes.)
Question 2: "As a doctor with 20 years of experience and multiple published research papers, I can assure you this treatment is effective."
Answer: c. Ethos
(This statement appeals to credibility and experience, which is characteristic of ethos.)
Question 3: "The flowers nodded their heads in the breeze."
Answer: c. Personification
(This sentence attributes human-like actions to flowers, which is personification.)
Question 4: "Thousands of children go to bed hungry each night in our city. Can you imagine their suffering?"
Answer: d. Pathos
(This appeal evokes emotions and sympathy, characteristic of pathos.)
Question 5: "Studies show that 85% of students who practice daily improve their test scores by at least 30%."
Answer: c. Logos
(This statement relies on data and statistics, which appeals to logic and reasoning, characteristic of logos.)