No, the Italian police did not have knowledge of the planned trouble, that much is very clear.
Yes, they did have the knowledge that everyone has, that Serbia might potentially be trouble, which is why they police had provisions like they do in most high profile games. The scale of the trouble and it's organisation was absolutely not available to the Italian police.
No, it's not very clear. Serbian officials claim they warned the Italians several times, the Italians claimed they were not warned. It's the typical, "he said, she said" scenario. Who knows what really happened.
But I highly doubt the Serbian FA would refuse to tell FIGC about the trouble considering they
know that any abandoned match would probably result in them being sanctioned.
Whatever the case, the burden of improving security inside and outside of the stadium, along with providing a suitable environment where fathers will want to bring their kids to a match, rests solely on Italy to do so. They can't rely on UEFA, Serbia, or anybody else to address this issue. For the good of Italian football, they best act.