Livebearers don't lay eggs. Only cories and loaches will do. However, cories will easily breed in your community provided you got 2 males and one female. That's the recommended ratio. With loaches, then your cory eggs will be eaten.
Loaches will also eat the fry of the livebearers but not the cories.
As for your barbs and tetras, you may not have cycled the tank hence their deaths. You need to cycle the tank in order for them to live without too much extreme changes in the water chemistry. Cardinals aren't suitable for tanks which are just establishing in the early stages.
Danios and platies are hardy fish and will survive during cycling. However, I'd recommend you go to Fishless Cycle
rather than cycling with fish.