1) No, that's definitely a mistake, keeping track of everything in putting this together is a struggle
2) Chaos Aura activates "when you are attacked", so as a reaction.
3) This subclass deliberately breaks action economy and many of the RAW mechanics for spellcasting. It might make sense to think of "accidentally" cast spells as Instant spells from MTG, and intentionally cast spells as Sorceries (Instants may be played whenever and their effect happens simultaneously with whatever else is going on, while Sorceries have to be played on your turn/take an action). Flavor-wise, your sorcerer is not casting these spells herself and doesn't have to worry about casting time because the spell just manifests itself from the chaos energy. As for getting unlucky and rolling a spell with a long casting time during combat, that's one of the trade-offs for being able to cast any spell in the list and having a chance to cast multiple full-action spells in a single round. You may have droughts where you just keep rolling non-damaging spells in combat, and you may have rounds where you hit three or more damaging spells in a row (I've had a combat where I cast Burning Hands, Lightning Bolt, and Thunder Wave in a single round).
Hope that answers your questions!