Hi, Charles. I'm very sorry about your difficulties. These type of issues are often best by contacting our support lines directly, especially the Technical Support by phone. In general, it sounds like you have some sort of multiple dropbox syncing thats a bit confused. This is really best addressed with a good phone call or screenshare by the tech support team. However, in the meantime, I'll do my best to address the issues you are raising:
1) I'm not really sure why it says the Autosave sessions folder has moved, very odd! I'd first ensure there is no Autosaved Sessions folder in your User/Documents/Accordance Files folder. If it is there, be sure to remove it! The actual Autosaved Sessions are stored in your user caches, but if Accordance keeps seeing an old Autosaved Sessions folder in your Accordance Files, it could be having difficulty managing it. They are not saved to Dropbox, so it isn't an issue that they don't appear in your Dropbox Folder.
2) The folders inside of the Dropbox folder are simply mirrors of what's online. They certainly don't contain any information Accordance is reading. Accordance gets all of your User Notes, User Tools, and Highlights from the User/Documents/Accordance Files folder - is this location empty as well? Also, is your content missing from Accordance itself, or just conspicuously missing from that Dropbox Folder?
3) The screenshot issue isn't one of Accordance, but of your Dropbox app. It can co-opt all of your Screenshots, saving them to Dropbox instead of your desktop. This setting is from your Dropbox app - Settings Gear - Preferences (see screenshot). Then go to 'Import' and uncheck 'Share screenshots using Dropbox'. I'm no Dropbox expert, but I believe this would be why they are being taken by Dropbox.
Let me know if this helps! But, if this doesn't get you squared away, please contact support. They'd love to help resolve everything.