As I understand it, you are right to say andar can mean "go" but in this example, if you use that translation, then you have degraded the quality of the information provided, as he could go in a variety of ways to school.
I'm jarred out by this as well. I understand that it's not the general iria, but if it wants specifically to say walk to school, then it should ask me for something that specifically means walk, like caminharia or even passearia.
"The student would walk to the school" is wrong but "The student would walk to high school" is right. Why?
The use of the article in "to the school" is incorrect unless the student is walking to a school that he normally does not attend. We go to school and we come home from school
This sentence using "would walk" makes little sense without context.
The student would walk to school whenever he missed the bus.
As a child, the student would [often] walk to school.