Probably best to stagger invoke at least 12 seconds. While you can have 2 Niuzaos summoned simultaneously, only one will trigger stomp when using purifying brew. Both can stagger damage at the same time, meaning one will take 40% of the initial, and one will take 40% of the remaining 60%. The end result is you take 36%, Niuzao 1 takes 40%, and Niuzao 2 takes 24%. But since you’re not in any danger of dying, to the point that you want to use purifying brew aggressively, then there’s no reason to be to overlapping.
As for 3, Master of Harmony has access to overwhelming force, which allows rising sun kick, blackout kick, and tiger palm to deal 25% of their damage in a frontal line, so you’re doing passive aoe, and more damage overall, by simply executing your single target rotation, espescially if you’re playing around with blackout combo. For shado-pan, I’m not entirely sure. Probably need like 7+ targets before its better to use spinning crane kick over single target abilities. You could never use it outside of an initial aoe pull and probably wouldn’t see a difference.
Stagger them. As Battlecruisr clarified, only one will trigger the stomp, which is a significant source of AoE damage. I usually go WoO → Invoke as the WoO buff will be present for the majority of both.
If you’re not in danger you could, but frankly it’s risky.
The only real time to press SCK right now is on pull, regardless of hero spec. It’s incredibly weak for Brew. Charred Passions had changed things slightly, however the talent isn’t played anymore past S2 4pc due to better options being available. Your AOE priority is mostly the same as ST; defaulting to Blackout Combo’d TP. Hopefully something that will change in Midnight, though we’ll see.