"They wrote a song for me."
Translation:Ellas escribieron una canción para mí.
That's correct, though a slightly different construction. What you wrote is "they wrote a song to me" or "they wrote (to) me a song." Either should be close enough to the English to be acceptable.
If you really want to say "for me" in the sense of a song dedicated to me, I believe that would use "por" and not "para." So, the use of "para" seems to indicate that the song was directed/gifted to me and not written on my behalf.
Yes. That is what David is saying. Using 'para' means the song is a gift to the person. Using 'por' would mean the song was written on that person's behalf. Both words have a slightly different meaning and both would work here because the English does not differentiate between the two.
"Me" is used when you are the direct object of a verb (Ex. "Ellos me escribieron una canción.")
When you are the indirect object following a proposition, like para, then you use "mi" (Ex. "Ellos escribieron una canción para mi.")
So your answer was marked wrong because it had an unrelated error, not because "ellos" isn't acceptable.
You also missed the first N in canción, but I'm not sure if that's a big enough typo to get marked wrong.
Perder mi tiempo atendiendo a las preferencias irracionales de un robot búho (sobre puntos sin importancia: la elección de un pronombre - "ellos" masculino o "ellas" femenino) resta del valor de DuoLino como una herramienta para aprender español y sugiere cierta pereza en la parte de sus programadores.