During our standard duty shifts (@20:00 UTC) we have both Missions (which affect the story) and Simulations (which usually don’t influence the story in any significant way). Simulations can occur outside of these duty shifts, though they are largely unscheduled.
Yes, we do use a mod for our sessions; to my knowledge, it does not work on mobile devices and is required due to the large amount of alterations and additions made to the standard game.