It seems almost to echo the sound of Pandemonium, though in a sadder and more reflective way: there is less hostility. Is there some connection between Ghaust and Pandemonium? Or is it to do with traveling to the past -- e.g. mirrors vs. fragments?

It's a little of both. when they go to the past via the mirror they go to the past in the midst of a war. At that time Ghaust began researching the Other World to use as a weapon, setting a date for an experiment. The trio happen to be there during that date, and the experiment goes horribly wrong. Instead of opening a doorway to the Other World, he opens one to Pandemonium, which they must stop from invading. As for the mirror and fragments, both are connected to Ghaust. The fragments just focus on Ghaust whereas the mirror focuses on the past in general.