Let's say in the distant future humans and aliens are going to school together, at least at a college level. If some of these aliens didn't have gender as we understand it, what questions might they have fore a gender studies course and how would we answer them?
The same questions that humans have with a more basic introductory course
It's important to be clear about two different concepts in answering your question. "Gender" is a societal construct that dictates how people behave in society. It is different from the sexual reproductive organs of a species. I'm assuming that you are explicitly referring to gender here since that's the focus of gender studies classes.
When worldbuilding, I like to start with the real world and see what changes are needed. So let's look at the Women's, Gender, and Sexuality Studies major at my alma mater. The first required course is "Introduction to Women’s, Gender, and Sexuality Studies." Students coming from a genderless society would probably have an additional prerequisite course called something like "The Concept of Gender" to introduce them to the basic ideas. Questions would probably focus on things like "Why do you enforce so many differences between the genders?" and "Where did this idea come from?" and "If it's just a construct, why aren't there more non-binary people?" Once they have the first basic course that introduces the issue, they'd be ready for the standard curriculum. Classes like "Psychology of Sex Differences" and "Sociology of Sex and Gender" would address a lot of the remaining questions.
I'm not giving specific answers to the aliens' questions because, honestly, I don't know them. I've been a human in a gendered society my entire life and I still don't know why I put bows in my baby girl's hair.
EDIT: Changed wording in response to comment from A Writer.