Re: [exterior]
Ah... Well, there was the usual spells and curses that ayakashi could use, and exorcism spells, and then there was higher level stuff like manipulation of reality and materialization... I don't think I learned much about their techniques though, since most of it is pretty much guarded secrets of their organizations.
That magic might be tied to the existence of that world itself though, since it was... kinda like a dream.