Quanto a quando ele sabia disso, há duas opções, ambas com argumentos válidos. Minha opinião é que a opção segundo está mais correta :
OPÇÃO 1 : Em OOTP, quando ele realizou a experiência "Essence divided"
Rosi: What does "in essence divided" mean?
J.K. Rowling: Dumbledore suspected that the snake’s essence was divided – that it contained part of Voldemort’s soul, and that was why it was so very adept at doing his bidding.
J.K. Rowling: This also explained why Harry, the last and unintended Horcrux, could see so clearly through the snake’s eyes, just as he regularly sees through Voldemort’s.
J.K. Rowling: Dumbledore is thinking aloud here, edging towards the truth with the help of the Pensieve.
LEAKY CAULDRON - 7.20.07 - WEB CHAT TRANSCRIPT
(hat / tip @Sthertherincess em esta resposta )
OPÇÃO 2 : Basicamente, desde o nascimento.
Isso pode ser deduzido de três citações:
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Relíquias da Morte, "Conto do Príncipe":
Another long silence. Then Snape said, “I thought . . . all those years . . . that we were protecting him for her. For Lily.”
“We have protected him because it has been essential to teach him, to raise him, to let him try his strength,” said Dumbledore, his eyes still tight shut. “Meanwhile, the connection between them grows ever stronger, a parasitic growth. Sometimes I have thought he suspects it himself. If I know him, he will have arranged matters so that when he does set out to meet his death, it will truly mean the end of Voldemort.”
Note que essa proteção "nós o protegemos" foi arranjada por Dumbledore do dia da morte dos pais de Harry , quando ele foi deixado na casa de Petúnia.
“You have kept him alive so that he can die at the right moment?”
“Don’t be shocked, Severus. How many men and women have you watched die?”
“Lately, only those whom I could not save,” said Snape. He stood up. “You have used me.”
“Meaning?”
“I have spied for you and lied for you, put myself in mortal danger for you. Everything was supposed to be to keep Lily Potter’s son safe. Now you tell me you have been raising him like a pig for slaughter—”... quando Dumbledore não nega isso.
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Outra citação é realmente uma que você forneceu da OOTP:
"I guessed, nearly fifteen years ago," said Dumbledore, "when I saw the scar upon your forehead, what it might mean. I guessed that it might be the sign of a connection forged between you and Voldemort"
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E, por fim, podemos deduzir que Harry teria que morrer do seguinte acontecer no final de Cálice de Fogo
When Harry told of Wormtail piercing his arm with the dagger, however, Sirius let out a vehement exclamation and Dumbledore stood up so quickly that Harry started. Dumbledore walked around the desk and told Harry to stretch out his arm.
Harry showed them both the place where his robes were torn and the cut beneath them.
"He said my blood would make him stronger than if he'd used someone else's," Harry told Dumbledore. "He said the protection my - my mother left in me - he'd have it too. And he was right - he could touch me without hurting himself, he touched my face."
For a fleeting instant, Harry thought he saw a gleam of something like triumph in Dumbledore's eyes. But next second. Harry was sure he had imagined it, for when Dumbledore had returned to his seat behind the desk, he looked as old and weary as Harry had ever seen him.Lembre-se que Dumbledore não se importaria com Voldemort absorvendo o sangue de Harry, com exceção de ONE e SOMENTE uma razão: aquela tomada de sangue era o que teria amarrado Harry à vida, permitindo que ele sobrevivesse sendo "morto" por Voldemort.
Como tal, a única razão para Dumbledore "triunfar", não importa até mesmo o cuidado, sobre o evento, teria sido se ele já soubesse que Harry teria que se sacrificar - e isso simplesmente lhe deu esperança de que Harry seria capaz de sobreviver a esse sacrifício.