Hey there, manes!
I'm really sorry to hear about your WD My Passport's fatal error!
I'd recommend you to try using another computer and see if you'd be able to access your files from there. Another thing you should definitely try is uninstalling and re-installing the external HDD as a device from Device Manager.
https://technet.microsoft.com/en-us/library/cc725782.aspx
If you have a spare USB 3.0 cable, I'd give that one a try as well and see if the error will appear then.
As soon as you gain access to your data, make sure you copy it somewhere else, so you'd have a backup.
You mentioned that the test is not finding anything wrong with the WD My Passport, however, I'd strongly recommend you to run the Extended test as well and share the SMART data results from it.
Keep us posted!
SuperSoph_WD