This piece seems to have several mistakes in instructions and in notation. "The first part is played again and then the third one" doesn't seem to make sense. It's too vague. Also, the D.C. should be a D.S. al Fine. That makes more sense of the two segnos. There should logically be a Fine half way along the 5th line, the bar before the repeat. In this way, the format makes more logical sense - play the page from beginning to end, then do the repeat from half way through the 5th line, until the D.S. al Fine (beginning of second to bottom line), then from the sign (b.7) and finish half way through line 5.
In notation, b.16 right hand should, I think, be the same as in b.32. Also, b.20 left hand should be the same as in b.19, and finally the 'B' in the left hand of the first bar in the final line should be a 'C'.
That's my interpretation of what may have been meant in this little piece, anyway.