Fe0xaech: I bought morrowind at this site for free, but I do not remember creating an account; or logging in at least. I realized if I lose the files right now, I will have to buy back. Any idea how can I register it to my account?
Morrowind has never been offered for free directly through GOG. Also, there is no way you could have downloaded the game from GOG without having created an account. That's literally not possible -- even GOG's permanently free games require creating an account before you can download them. If you have a GOG installer for the game but have never created a GOG account, then you have downloaded a pirated copy from an illegitimate site.
However: the game was legitimately offered for free -- AND COMPLETELY DRM FREE -- through Bethesda a few years ago through their Bethesda.NET launcher. Maybe that's where you obtained the game?