speculation: the event name, magicians assemble*gathering of the 3 magicians, may refer to switch's formation, as they refer to themselves as magicians and this was switch's first major event, which introduced them to the game.
the story name, element, may refer to the elements alchemists use in their scientific "magic." switch songs refer to alchemy, and natsume has noted he is more interested in alchemy as his preferred sort of "magic."
Even in Hell - 1-8
the title of these chapters is part of a japanese proverb — 地獄の沙汰も金次第 or "even in (the affairs of) hell does money make a difference/depends on money" which basically means as long as you have money you can do anything. even in hell!
as a note, it is now autumn while the events in "even in hell" were back in spring. you can also see eichi's stuco badge on his lapel now!
nagisa and hiyori, as you can guess, are the members of old (current in this case) fine. they have not been mentioned in-story before but it's safe to say that this scenario probably won't be the last of them.
Ash Returns to the Sky - 9
if you don't know and you wanna see what happens immediately after this boy have i got just the thing for you