Bravo. Your translation has the spirit of the song and that is what matters most . Is it correct to translate the title "I understood that you loved me"?
By the way there is another translation that feels like a collection of random words.
My love of this song goes back 50 years ago, when I was a teenager in Tehran. I used to hear his song over the radio and I loved it and I tried to sing along mimicking the words without knowing their meanings. Now tanks to the Internet and Google and You that have brought me the meaning of the song . It is just as beautiful as I always guessed all along.
Ciao
I took some liberties here in the translation. There are many "frasi fatte". Or sentences that have a meaning beyond what the words say.
I am starting to see what it took to translate the Iliad and Odyssey from ancient Greek to the modern languages and keep the meter going.
I still hope you enjoy it.