They discuss the crack in the wall, he doesn't admit to anything including being a policeman, and the whole time Amelia's trying to get to the point -- this crack in her wall -- he's spazzing out, post-regeneration: "Still cooking," as he says it. In terms of demonstrating how charming this Doctor is, you couldn't do better than staging him as the backyard E.T. to the cutest little girl that ever lives. On the other hand, it's half the episode.
"Does it scare you?" he asks, she thinks, about the regeneration issues -- that gold stuff coming out of his mouth, the sudden hungers and cramps all over -- but he's taken the measure of her enough to know she's pretty unshakable: He means the crack in the wall. Absolutely, she agrees, and she's so serious that it means something to him, which means it means more to us: This little girl doesn't screw around. If she says the crack is an issue, then we'll deal with it. He hops up from his knees and grins with relief: "I'm the Doctor. Do everything I tell you, don't ask stupid questions and don't wander off." Then he walks into a tree.
"If you're a doctor, why does your box say POLICE?" HE is too busy being adorable. He takes a bite out of the apple, spits it at her face, and says that no, he hates apples. How about yogurt? Spits in her face -- "I hate yogurt, it's just stuff with bits in!" -- and explains that he has a new mouth, with new rules. "It's like eating after cleaning your teeth, everything tastes wrong." The music reminds us that this is all very droll and sweet, and he goes, "You're Scottish, fry something." Bacon, he hates, Beans are "evil." Bread and butter gets tossed in the yard, complete with a meowing cat. We're still not done, and the music is getting wilder all the time, and we hate carrots, and it turns out that what the Doctor needs is fish fingers and custard. Wacky!
They sit in the kitchen while he dips his fishsticks and discuss each other. She tells him he's funny -- but in the way a forty-year-old police sergeant might -- and that tickles him. He likes her name, Amelia Pond, because it's like a fairytale. She's Scottish, but moved with her aunt to "rubbish" England for some reason. The Doctor commiserates with her parentless status, pointing out that he doesn't even have an aunt: They agree, childlike, that he's lucky. The Doctor doesn't mention that his family is bullshit and molested his best friend through space and time in order to end the entire universe, because that's not a conversation you can have with a little kid. Not even an absurdly special kid like Amelia could handle the total bummer that is the Time Lords.