At Mondo Verde in the Netherlands, which I visited in August of 2018, they had a pretty decent (several dozen) Egyptian fruit bats (Rousettus aegyptiacus) kept free-flying in their tropical hall (although I only saw them at feeding time in the afternoon) alongside quite a few bird species, including pigeons, ibisses, ducks, starling-type passerines, trumpeters and macaws. I did not see any interaction and the birds (apart from one passerine) kept their distance from the feeding bats. It seems that keeping bats and birds together in a rainforest hall is not uncommon and can definitely be done.
As far as crocodilians in a rainforest hall, I guess they would do well as long as the environmental conditions match their needs. With regards to birds you would likely have to keep the crocodilians in a separate area where the birds cannot go to prevent the crocodilians from chomping birds that land or perch in or near their enclosure, which they would definitely do given the chance. Mondo Verde and Burgers' Zoo in the Netherlands both keep caiman in their tropical halls, and in both instances the caiman were kept in a section or exhibit netted off from the birds.
I did however see free-ranging birds kept in the crocodile and hippopotamus house at the Beekse Bergen without any barriers between the birds and the Nile crocodiles. However the birds kept there were only small fast-flying birds like weavers and starlings and their areas of interest were mostly outside of but also partially directly above the crocodile exhibit (branches with nests). The Rotterdam Zoo has a somewhat similar situation in their crocodile house, but that house also has a substantial area with other animals (hyrax and porcupine) where the birds can go.
I think smaller birds are far less likely to perch or land on or near the water and would also be quicker to get away than, say, something much more substantial like a duck or an ibis that is also water-oriented. Bigger crocodilians would likely target larger species a prey, but might not bother with small birds. That said, small or young crocodilians could perhaps target smaller birds as well. So in general it would likely be better to keep crocodilians in a bird-free area, or to at least to give the birds a substantial safe area away from the crocodilians.