Well, at least I've just discovered that the two issues I mentioned I was having ARE NOT RELATED. In fact, one of them is, as suspected, a problem not in the flash card nor the iPod, but in that increasing pile of bugs that is iTunes.
The tracks that are syncing over and over again are those who have the field "Work" filled with any data. As soon as I deleted that, the problem disappeared. Of course this is going to be a huge PITA for those who have huge collections of classical music and depends on this piece of metadata to keep their libraries organized. But it's either deleting that field or waiting for Apple to fix this bug.
I hope this might be useful for somebody!
EDIT: regarding the problem with the songs playback being cut off early, I'm 100% now it is due to something in the iTunes/iPod software part. See:
https://discussions.apple.com/thread/7249051
What I find weird is how this problem get transferred to the iPod if the iTunes library file was deleted a long time ago and everything goes well in my Mac.