Yeah, the edges of Other-Tokyo is enveloped by a thick fog. Wandering into the fog will just have you end up back inside the city. Lore-wise, it isn't understood how any of the inhabitants came to be. They were just always there since the conception of Other-Tokyo, which is still being researched by Black Babel. The badges contain a special Craft that facilitates the dimension hopping, but since only Witches can use magic, they're the only ones who can access the badge's magic.

Magic works like superpowers basically, except it's an inherited trait. At least one parent must've been a Witch. You don't learn magic. It's just discovered naturally as you age and there are no resource (like mana) behind it's use. Black Babel has Daemons that can detect if a person can use magic.

There are no differences between a Witch and a normal human aside from the ability to use magic. Most Daemons are very much instinct driven like animals so they are handled in a similar manner. Some Daemons like Familiars are intelligent and are drawn to a Witch's magic. If a Familiar likes you, it will seek you out to form a bond.