Why are you looking in /root? That’s part of the operating system of the MyCloud, and you shouldn’t really be fiddling with it.
Your user data will be found under /DataVolume/shares, or just /shares (there’s a defined shortcut)
I wonder what that prog-1-jan-2005.tar.gz is. Do you have any non-standard software installed on your device? Something that downloads TV programmes…? Because that’s what I suspect that prog-1 thing is (1.3GB is about right for a TV programme). And it’s filling up your /root drive, and probably causing the system to have problems.
If you are using some sort of torrent downloader, you may have configured it incorrectly, and it thinks it’s on a desktop Linux machine, where all partitions are the full disk space, so it doesn’t matter where it puts data. Not so on the MyCloud: you need to get torrents put into the user space (somewhere in /shares).
If you want to remove it, do this:
I can’t check my devices at the moment, but I don’t think that prog… should be there.