Shadow damage is a holdover from D:OS1. It's not actually used in D:OS2 and may not be supported everywhere.
A weapon or skill with "chaos" damage randomly selects a damage type from Water, Air, Earth, Poison, Fire and Physical (see Chaos Bolt for example).
Yes, it is possible for a status to take instant effect, at least for DAMAGE and HEAL-type statuses. It's what the DamageEvent or HealEvent entry is for.