When I upload an InDesign file with many layers, the cloud doesn't allow me to edit anything. Can someone tell me how to access the various layers such that I can change content, photos, etc? All I see is a flat, static image of the first layer and nothing more.
If you're talking about the File Sharing for the Adobe Creative Cloud, it's not intended that you be able to edit the file "in the cloud." Editing an InDesign file must be done by opening the file in InDesign CC on your computer, or if you share the file with someone else, on their computer.
What you see on File Sharing is just a preview image as you have seen. Log in to creative.adobe.com, select the file and either download it or use the Share feature to post it publicly or send a link to another person.
What you are seeing on the Files page of the Creative Cloud is just an image exported from InDesign.