In my head, but possibly not on the page, Alice's very, very fragmented remaining memory knows who knows how to retrieve her, and that that person likes this particular sweet. She doesn't know how to offer a different clue, and so she keeps trying the same one over and over reflexively, and she keeps offering it to the one person she is absolutely and instinctively connected to.
Age difference: she didn't say her whole thought, which was, the age difference between me and Harry is ~22 years, and the age difference between our boy/girlfriends is five years ack ack ack.
As to adultish busy Harry, as much as I love flustering the boy (heh. I like flustering nearly everyone), I also like making him basically competent and strong, once he has a more normal role in the world (that is, being in charge of a bunch of fixing and rebuilding and appearances and stuff at 18 is not that normal, but comparatively...). And good at taking care of people, including going all Don't Piss Me Off where necessary, just because if it's the capacity to love that makes him able to do the insane task he's been destined to do, it sort of follows that the trait would be central to him.