:iagree:Hoo-boy.
I can see it as both a nitrate and ammonia and aggression problem. It sounds to me like you overtaxed the tank's bioload about 3 times over when you added them all. This could cause a spike in ammonia or nitrite/ate. How long had the tank been set up before this?
Telling males and females apart in tiger barbs is fairly straight forward, the females are much rounder and the males tend to be slightly more vibrant. I have also seen people say that when spawning the males get red noses, not sure on how reliable this is though.
By "black tetras" do you mean G. ternetzi? These have long fins which are deffinitely targets for the tiger barbs, especially so when the tigers are stressed.