I am organizing a quiz for a university math class with more than 100 participants. The quiz will consist of several essay questions, where people will have to upload images or PDFs of their hand-written calculations.

Please offer a way to download all the uploaded files per question at once.
For random questions, the download should make visible which question was answered.

My workaround would be to replace the quiz by separate assignment activites for each question. Those offer this bulk download at their Grading page under "Grading action: Download all submissions".
In order to use random questions, the workaround would be to have both the quiz and the corresponding upload activities. For grading, one additionally has to examine the quiz results to determine whether each student answered exactly the question assigned to him/her.