In the end I managed to solve this bug.
It was easier than I expected, and, as usual in these situations, you always look for the most difficult solutions forgetting the easiest one back.
For some mysterious reason it seems that OGP only likes thumbnails which dimensions are the same or more than 200 pixels. The fact is that when you upload an image on WordPress and set it as thumbnail, it will be resized to, by WP defaults, 150x150 pixels.
In my case, the easiest solution was running the Facebook debugger which in turn gave me the ultimate hint on what I was lacking.
Actually (forgive my hilarious madness) I was definitely lacking in size.
After running a scan, I got this message:
Open Graph Warnings That Should Be Fixed
Small og:image: All the images referenced by og:image should be at least 200px in both dimensions. Please check all the images with tag og:image in the given url and ensure that it meets the recommended specification.
So I manually enlarged a random thumbnail of one of my previous posts to the actual 200x200 pixel size and tadadah!!! Size DOES matter!
Facebook now shares the proper link and proper image also from WP homepage or single post without hacking any code. Hope this can be of any help to everybody has the same issue!