"They wrote a song for me."

Hmm. Not sure - whether it is or if it is why? Perhaps ambiguity w/o other info - eg maybe ustedes. Also does the "for me" require para? Not sure about that. They wrote [to] me a song seemsbok really. Be interested to see other thoughts.

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.

usually from context but in this case ellos or ellas are correct if it doesn't make sense in context then you wouldn't know because they are conjugated the same