How hard is JpCC actually? Will we be able to complete all the content with our Coro/Sulstan/Selene parties?
No.
I gues some people will disagree with me, but after finishing the story so far I don't think the Continent of Sins is doable with a warrior team. You needen't worry about that, though, as it is the latest content.
As for events, the answer is still no, for some of them. Having different teams composed of different arcana (different classes) is actually needed in some, but is not the norm.
The mission system introduces some nasty spins, for example, the mission we were comenting on is a hard lvl 45 free quest, but their spin is to ask you to take it on with a single arcana (+ a friend's) in order to get 2 tickets upon completion. It can be tackled as a run of the mill free quest, but you won't get the tickets that way.
There is also a special ruleset for some quests (only archers, only mages, max 40 cost, etc) that can be mandatory - this is more common.