OK..so I downloaded the songs on a computer in .mp3 from YouTube (because I was in a rush) and sent them to my phone. Then, when I was going home, another surprise. Even if the downloads from YouTube are not done in a very high quality, the .aac songs were more that OK. But the mp3-s were worse than anything else. I had difficulties in even understanding what the singers were saying. So, Google screwed it up a little.
What you have to do is to download the music externally (not from YouTube, because they are mainly in a low quality), preferable is directly in .mp3 (because converting can affect the quality!) and then to send them to your phone. You can send them via your USB cable, but as I observed that the media player "feels" the changes with a considerable delay, I recommend you rebooting the phone. If it still does not see your music and you are sure it is in .mp3, play a little with the player and then it should update the list with the new songs.