You beat me to the second. They had to die by the hand of one other. So the basilisk couldn't have killed harry since the basilisk is not He-who-must-not-be-named.
The Horcrux that was part of Harry was in his soul. The basilisk fang entered his physical body. Two different concepts. By Voldemort "killing" Harry, he released his soul, as well as the Horcrux attached to it. But the venom couldn't reach Harry's heart.
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