Sony Xperia Z1 randomly rebooted and when it came back up, apps on the SD card read "Application not found"
Maybe I can help with part of your question.  I too have had a 'Not Enough Space' issue.  I deleted a bunch of files and off-loaded more, still I could not move or edit other files.  Going to settings and checking 'Device' 'Storage' the operating system indicated that I had over 2/3 of my internal memory available. 

I found that if I power cycled the device it would reset the file space available counter in another part of the operating system.  I also found that I could not count on my deletions or moves being deleted or moved unless I used the Power Cycle trick very soon after preforming the deletions or moves.