Well first, some of the songs that you put in, well...Sony Co. cannot transfer directly, so you would have to use their Sonicstage program, aka the converting button.
Like most Sony mp3 players, you need to use Sonicstage to put songs in the mp3 player.
For the Sony NW-E405, simply go to the Transfer menu at the top right of the program, (along where the My Library button is) and select the song. In the middle of the screen should be arrows along with a suitcase looking button. Click the luggage button and a screen should pop out. It should have two choices, a Standard Transfer Mode and a Specified bit rate transfer mode. Click the Specified one and select either the 105kbps (ATRAC 3) or the 132kbps (ATRAC 3) for great sound quality and small memory usage. The others are too big or too bad for sound quality. It should now work.
Now the mp3 player should be able to read it, since it is now in ATRAC 3 version, not the mp3 version.
For the songs with no data, the songs are unquestionably banned from the Sonicstage program either because of illegal data in the mp3 songs or the corruption of the data itself. It happened to me quite a lot.
You could try converting it like the top section...some of those songs worked.
Hopefully this solution helped.
Have a nice day!