Ok.. so I got it to work for me. I'm going to try explaining it for those in the exact same situation.
I restarted all the exercises one by one moving backwards and started again. I even created a repository with the same name provided in the example (user-name-cc.github.io). It is weird that the first instruction is met eventhough it says "No such file or directory".
Because it says "No such file or directory" I create a personal-website and then change directories to it.
I do the "git init".
Then I copy the sentence in the 'Learn' section (git remote add origin..), just changing the Github user name in that sentence to my GitHub account name. Here is the 'tricky' thing. The url we have to type ends by 'github.io.git' eventhough the repository we make in GitHub ends at 'github.io'. So we need to add '.git' at the end of our repository name!
I didn't do that before I think..
From here on I just followed the instructions.
I hope it helps!