The mimicking of caterpillar appearance AND behavior is really interesting! Also, what's the purpose in the parent waiting for a significant amount of time before handing over the food? Is she looking out for predators, so that they don't see her "feeding" her "caterpillar"? The nest is also pretty inconspicuous... Just a pile of leaves, and some sticks. It doesn't look very much like a traditional nest. Helps with the illusion that it's just a caterpillar sittin' on some dead leaves. Also, at 4:08... is that a poop/pee packet? That's pretty cool that the nest is kept clean by letting the mother take it out manually.
the white thing that came out of the baby is a fecal sac, the mother took it away to help keep the nest area free of smells that could attract a predator.