After several days trying what people have been suggesting here (connecting with Ethernet Cable instead of wifi, bypassing, etc.), I've finally resetted my password with my Apple ID.
As some people mentioned here, if you try using Apple's support, they'll say something like "This error was not supposed to happen, it's impossible, it just doesn't happen, you've gotta keep trying until it works", and stuff like that. So, they don't have the slightest idea why that error keeps occuring.
My last unsuccessful attempt was trying to hack my hard drives via brute force, but after several days without a result, I finally came with the idea of trying to reset my password from another Macbook Pro (mine is from 2011, the one I used to reset my password is from 2014 and has all OS updates). In other words, I took my hard drive from my Macbook Pro, put it in a hard drive enclosure with USB interface, plugged the enclosure to this 2014 Macbook Pro, and tried to boot from that hard drive (restarting the system and holding the option key until the system asks us to choose a hard drive to boot from). I've tried some passwords until the system suggested me to reset password using the Apple ID, and followed the instructions(a wizard opens, then asks the reason why you can't log in with your password, then I chose "I forgot my password", etc). And it worked, without the errors I've reported.
How/why did it work, I don't know, but it seems that newer Mac OS X versions "don't like" old Macbook Pro's.
So, in other words: if you have an old Mac and forgot your password, it seems that the solution is to remove your HD from that Mac, put it in a HD Enclosure, plug it in a Mac that is new and has everything up-to-date, restart it with the option key pressed, choose that HD, and then follow the "reset password with my Apple ID" steps.
