Translation:The Italian woman shouts down onto the street.
No shouting onto a street is not grammatically correct. Onto implies physical contact. A shout is not considered physical (even if the shock wave of air is).
"Shouting down onto the street" sounds pretty weird to me (native US English speaker). I was happy that it accepted "Shouting down to the street," which sounds normal to me.
It makes sense in English. I would understand it as the woman (perhaps she's on the third floor) shouting down to the people at street level. I could be wrong, but that's how I would understand it.
No, shouts down to the street. Onto would mean she moves there herself, which is not what happens when you shout.
I think you will find this is another one of those differences between English speakers and "American" English speakers. both "to" and "onto" would be acceptable depending on where you came from.