re: A few questions from GoT Hardhome (Spoilers, books? etc).

The show has not actually explained that the White Walkers cannot pass through the Wall. "The Wall protects itself", indeed. It was built not to keep out Wildlings, but to keep out the White Walkers. This has simply been forgotten over time due to the petty concerns over ordinary mortality and the ancient history of the story of the Long Night. I hope that the story of the Lone Huntsman is eventually told in the show.