They appear to be Blaberus colloseus - Colossal Cockroach or Blaberus giganteus- Giant Cave Roach.

They can flutter, not really fly.

I feed my roaches ground Dog Food, Rodent Lab Block, Oatmeal, Kashi Brand Cereals. It smells quite good once it's blended.

I'd keep a heating pad on their enclosure, it seems to speed up reproduction. Generally temperatures in the 80's - 90's seem to work the best.

I offer them fruit and veggies for their moisture.

I don't like the water pillows because of the build up of bacteria. The cricket gel cubes have scared me ever since people lost entire feeder colonies a few years ago from using them.

Hope this helps.