Ria Redwood Images that have been imported will only be available in the current Fashioner session after import. We don't save the imported files, so we don't have access to them when you re-open a Fashioner session.
You need to finish up your work with the imported image(s) before you close the Fashioner, or before it times out. When you try to open a Fashioner session that had an imported image, it will show the image not found icon, which is what you see X3 in your screenshot above.
Your only option is to use the Layer Visibility tool and hide these images. Then re-import them again for use in the open session.
I have not had any problem moving an image after import, so I'm not sure what is going on. I use the Chrome browser on a Windows PC.