I think it would be great if we were able to study specific sections of a list on the Apple app.

I have a student I'm tutoring. To help her study for her Chinese tests in school, I make her lists and have her study them. It'd be great if I could make one list and let her study just one section of that list, rather than making a new list each week and her having 40 lists at the end of the year.

Jeremy, you can do this in a different way (I do this for my wife, she has now also started studying).
Let's say, you have a list A, which is the complete list with all items to be studied over time. Give your student a list B, which the student should study and which contains the currently relevant vocabulary. Then go to list A and select the next items to be studied by either selecting item by item (click the small box next to the item) or select all items from the section by clicking on the top left small box. Then select from the top Words Action... the Copy to List and copy all these items to your student's list B.
This list B might become quite messy over time because all different items are in there. But once your student has learnt all items from your complete list(s), you can delete list B and activate list A for your student, so that the student still goes on with the reviews.
I am doing this with existing lists. E.g. I take the list of radicals and watch out, which characters she has learnt and which radicals would now be helpful for her. The same I do with a list of measure words, which I have prepared. So her learning list might be a combination of different lists.
The other possible way is to give your student the complete list, but you ban the words, which are not necessary to learn now (also in the Words action). Then you can slowly go and unban the words which should be studied now.
If you need further explanation, feel free to drop me a mail.