Yes he does, but not until sometime in the 7th book.
the fact hat the diary was a horcrux but no one knows it yet
No she didnt....Dumbledore tells Harry that he is a Horcrux
No, he didn't die because he was Horcrux. Had he not been a Horcrux the killing curse would have killed Harry, instead of just the Horcrux.
the fact hat the diary was a horcrux but no one knows it yet
I guess you mean "Voldemort"? That's because Voldemort tried to kill Harry, but when he did, he actually made a Horcrux. Harry is the horcrux, but he is Harry as well. The Horcrux inside Harry gets killed in the last book.
Yes, the horcrux inside of Harry Potter
He suspects but he isn't sure. Harry knows that all the founders of Hogwarts had items. He knew that Salazar's locket was a Horcrux and because Tom Riddle/Voldemort thought of Hogwarts as home it made sense to make them into Horcruxes. However, the diadem was 'lost' so Harry wasn't sure even Voldemort had found it until after reading Voldemort's mind he found out where it was and that it was a Horcrux.
No, but the diary Horcrux, was destroyed.
It depends what Horcrux your talking about, they do find them all and destroy them all though.
The Ring
yes
The diary