This is a bug described here.
It involves the fact described here.
Synapse broke how things work with files with executable permission.
If it has executable permission it tries to execute file instead of
opening file with relevant app.
So, as said at that link, a solution would be to remove the executable permission for all such files or, as said here, add
noexec in the options column of
/etc/fstab for that partition.
I prefer to use "Disks" (
gnome-disk-utility, can be run as
gnome-disks) in order to automatically mount that partition.
So, in "Disks", selecting that partition and its mount options, (where I had already) unchecked the defaults and checked to mount at startup (setting a mount point): the solution was to add
noexec at the list of options for that partition.
After reboot Synapse was able to open all files in their relevant applications.