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As Voldemort Disapparates, they came out of the woodwork and Harry and Snape exchange an understanding look, Harry gathering Snape's memories that poured from him as he died there from Nagini's poison. Snape was bitten in the neck, not snake food or Snape wouldn't have lasted long enough to give Harry his memories. Nagini did not come out of her floating magic ball. The ball rolled onto Snape as the upper half of his body was contained in it. I don't think Harry and Snape exchanged understanding looks. Harry was shocked and Snape was bleeding to death.
Harry Potter and the Half Blood Prince is the book where Dumbledore is killed by Snape willingly. Snape is killed by Voldemort in the Deathly Hallows because Voldemort thinks Snape controls the Elder Wand but it is really Draco Malfoy because he disarmed Dumbledore at the top of the Astronomy tower in the HBP. Hagrid does not die.