zebra and leopard danios are basically the same fish, and yes they will hybridise and yes the offspring are fertile (they tend to look similar to zebras). The origins of the leopard danio are obscure: they were originally described from specimens with no locality data -- there are suggestions that they came from Thailand or Cambodia, or that they are actually a mutation of the zebra danio bred in Europe. DNA tests tend to support the latter, but its really all up in the air.
With regards to breeding the tiger barbs and danios in the same tank at the same time, might as well give it a go and see how it works. Personally though I'd just breed one of them, then when the breeding tank is freed up again breed the other.