What happens to student submissions that include file uploads? Is there a folder where submissions are stored?

In Canvas, there is no concept of storage folders for Assignments.

You access file submissions via SpeedGrader. For compatible file types, SpeedGrader will open the document within your browser, where you can annotate/comment directly.

You can download all student submissions for an assignment.

You can check the submission status of an assignment using SpeedGrader or New Analytics.