They don't "do" anything during the fireworks but continue the show, AFAIK. You can't hear the fireworks (well the music I mean, I suppose you could hear the booms but not that loud at all) from the luau area.
Fireworks on party nights have always been at 9:30.
On other nights of the year, fireworks vary by day - depends on park hours, how many parades are offered that night, etc. You have to check that day's schedule.