Once a section has been downloaded, you should see the green cloud with a check mark only on the sections you have downloaded. You can also go to the options at the top and open the "Manage storage" page, where you can find and remove any individual sections you have downloaded. This should be working properly because we haven't had any issues and the app hasn't been updated for months (we're releasing a new version in a couple of weeks).
On the other hand, about the old files, even if they are not embedded within the page, they will be downloaded if they are available in the editor. You can remove them going back to the editor and opening the files manager, in three steps:
Open the files manager (the button before last, after the video):
Click on the file you want to remove (in this case "landscape-small.jpg"):
Click the delete button at the top, and confirm the operation: