I would say the teacher is correct.
Think of it like this, you are not taking a sample of people from a population of people; rather, you are taking a sample of measurements from a population of measurements. In regards to your problem, we are only interested in the recorded response of each person; however, you wrote (for part c), “voters in his district that gave a yes or no response,” which implies your population is a collection of voters (people). If you would have said, “the response of voters in his district,” then clearly our population is a collection of responses (measurement on the person) and not a collection of people.
For example, if you want to study the height of a certain tree in some area, your population is the height of every tree (not the collection of every tree) in the area and your sample is a sub-collection of heights from the population (not a subset of trees from the population).
Does that help?