this is a tough question and a tougher answer,
I will go with logic and odds on this,
its possible to get a bad fish, or it get stressed out and just do poorly, so lets say 50% of the time this was the case as its unlikely your luck would be this bad especially since you come to me

, I could believe the blue tang and the mandarin could fall under this situation for a example. But the engineer and the puffer should have been pretty stout and do amazingly well in tanks as a rule. So that leads to the parameters of the tank or the tank mates. I know you care for your tank and can test and ITS very likely that old tank inhabitants are hazing the new comers to the point of not eating and dieing or just plain being beat to death.
Likely fish to do this in your tank from my experience:
two clown fish (esp if its a tomato, sebae, or maroon but I have even seen very mean percs) one basslet, one damsel, either one of those two can most definitely be killers after making the territories in the tank. so pretty much every fish you have can POTENTIALLY be dominate and territorial. ( it does not help that the tank is approx 30 gallons as space is divided up quickly with bullies) If you can identify them bring them back and trade in or we can do a hard reboot and bring them all back and start over with small fish.