I FOUND THE SOLUTION!!!
Ok settling down...
. I didn't do the selective startup but it was a good idea. I'm using a program called Gamebooster when I wanna play games, as it stops unnecessary windows and non-windows services while playing to boost the performance.
By chance I tried the HDD with Gamebooster on, and it worked! So after looking at the blocked programs, I found that the culprit was Acronis Drive Monitor
, a program I installed a few months ago and that is supposed to tell you your disk's health status. It loads with windows so that's why I always had the problem. I did a quick online check and it came up with this WARNING - USB Drives may not work when Drive Monitor is installed | Knowledge Base
, apparently it's a know issue.
I have now uninstalled Acronis and my disk works like a charm. I still don't know if I'll get the BSODs but I'll get back to you if I do. It still prompts me for admin permission if I wanna transfer a file in the HDD primary folder, but not if I want to create sub-folders or transfer a file into sub-folders. Maybe it's always been there, I don't mind cuz now it works fine.
Finally after 5 months the issue is resolved. Thanks a bunch for the ideas John and merci beaucoup kesume, every time you see me you jump on the occasion to type 1 or 2 french citations ^^