The half demigod and half witch

Prologue

A neighborhood on a street called Privet Drive. An owl sitting on the street sign flies off to reveal a mysterious old man walking through a forest near the street. This man was tall, thin, and very old, judging by the silver hair and beard, which were both long enough to tuck into his belt. He wore long robes, a purple cloak that trailed on the floor, and boots with slight high heels and buckles. His blue eyes were clear, luminous, and sparkling behind half-moon glasses, and his long and crooked nose, as if he had broken it at least twice. His name was Albus Dumbledore.

Albus Dumbledore did not seem aware that he had just stepped into a neighborhood where everything from his name to his boots was frowned upon.  He was busy feeling the cover, looking for something. But he seemed aware that he was being watched because he suddenly looked up at the cat sitting stiffly on a brick, which continued to stare at him from across the street. For some reason, the sight of the cat seemed to amuse him. He chuckled and murmured.

DUMBLEDORE: I should have imagined.

He found what he was looking for in the inside of his pocket of his cloak. It looked like a silver lighter. He opened it, lifted it into the air, and lit it. The nearest street lamp went out with a dull click. He turned it on again - the next lamp blinked and went out followed by many others surrounding the neighborhood. The only lights in the neighborhood were two tiny dots in the distance. The eyes of the cat that watched him. Dumbledore put the 'lighter' back in his cloak and walked down the street towards number four, where he sat on a brick wall next to the cat. He didn't look at the animal, but after a while, he walked towards it. 

DUMBLEDORE: I imagined meeting you here, Professor McGonagall.

And he turned to smile at the cat, but it was gone. Instead, he found himself smiling at a stern-looking woman wearing half-moon glasses. She, too, wore an emerald cape. She had her black hair tied in a tight bun. And she looked decidedly irritated. 

McGonagall:  How did you know it was me?

DUMBLEDORE: My dear professor, I have never seen a cat sit so stiffly.

McGonagall: You would be broke if you had spent the whole day sitting on a stone wall. All day? When I could be celebrating? I must have passed more than ten parties and banquets on the way here.

The teacher sniffed in annoyance.

Dumbledore: Ah, yes, I saw everyone is celebrating.

McGonagall: It was expected that they would be a little more cautious, but no, even the muggles noticed that something was happening. It was on the news. 

She nodded towards the Dursley's darkened room.

McGonagall: I heard... Flocks of owls... Shooting stars... Well, they're not completely idiots. They couldn't help but notice something. Shooting Stars in Kent, I bet it was Dedalus Diggle's doing. He never had much sense.

Dumbledore: You can't blame them. We have had very little to celebrate in the last eleven years.

McGonagall: I know that. But that's no reason to lose our heads. People are being completely careless, they take to the streets in broad daylight, without even wearing muggle clothes, and they spread rumors. It would be funny , if on the very day that You-know-who seems to have finally left, the muggles discovered our existence. I suppose he really gone, isnt he, Professor?

Dumbledore: He is indeed gone.

McGonagall:  Are the rumors true Albus ? What about the girl?