I first tried “ue4-mp-downloader” (as it was the first result on google) but it did not work. Things may have changed and it stopped working.
Then I found this unofficial UE4 Launcher on the Unreal Engine forums, and downloaded a few things w/o any problems!
I used a Google-linked account as a sign-in method (just in case you try something else, this method is working!).
The real problem is that I have already posted this answer on the Unreal Engine forums, but my posts are awaiting approval and I read that may take more than a month! So, as many Linux users are struggling to download even things they bought, I post here in the hope they reach here somehow when they google again about it!
I also wonder if there are any other alternatives? Also, helping to keep any of these projects updated (working) would help a lot!