The Blacksmith is the Tree's avatar.
She helps those who undergo Ascension choose whom they wish to be next.
Unless someone from outside the Ever After has a desire to leave, they cannot go through the Door. As Neo lacks a purpose now, she cannot serve as the Cat's vessel; so she keeps bouncing off the energy passage.
The Curious Cat's riddle "it's not a place you go. But a place you know" means you can only reach the Tree by giving in to acceptance.
While never stated, Alyx and Lewis come from before the Great War of Remnant. As their names do not follow the Color Naming Rule; which was established in-universe to remind humanity that art and creativity cannot be eliminated. In the real world, Monty Oum's instructions for character names were that they were a color, meant a color, made you think of a color, or sounded like a color; in any real world language. But only for the present day humans.