I've noticed two inversions associated with 'say' in the song.
"So to her mother, Tommy said"
So, Tommy said to her mother.
"With his dying breath, they heard him say"
They heard him say with his dying breath.
1. Does a native speaker use it(the inversion in question) in their regular writing/speech?
Tell Laura I Love Her Lyrics
No, people wouldn't speak that way in normal speech.
It's used to help the song flow and sound better.