Data partly lost or hidden on external disk
I have solved the problem connecting the disk directly via SATA, I didn't have a Macintosh to install a 3.5" disk into, so I connected it to a PC with Windows 7, installing the HFS+ drivers, which allowed PC to see the disk and read (but not write) the data on it. I was able to copy the data to another external disk which I formatted into exFAT, so it could be used with OSX and Windows both. I still don't understand what was the problem with the disk, but I saved the important data, so I consider the problem solved.