In a literal sense, I think Don is right and that it is a two-parter, with the answers given in turn. I did not exactly take it to mean that school information is needed in order to process payment.
However, the Q&A does conflate the two issues. I can definitely see how students, many of whom are ESL and don't read as well as I do, would get the impression that if they don't put the name of their school, they won't be able to place an order. The absolute most generous explanation I can think of is that the writer of the Q&A was artless. Otherwise, I'd strongly suspect disingenuousness.
As to knowing the school and course: To me as a writer, it's often helpful to know the type of school, because expectations can be so different at upper tier vs. community college vs. online proprietary. In fact, that's all you need to ask: "What type of school are you attending?" perhaps followed by "What type of class are you taking?" The name of the school is irrelevant.
This information you're collecting about the school and the course, are you passing it along to the writer? Because otherwise, I have a hard time seeing how it would benefit the paper.