They will stay in there I presume. This was formerly used for adult cassowaries (a few years ago) so the barrier is obviously good enough, but it looks remarkably insufficient. I'd imagine any adult cassowary could clear it easily if it so desired.
I would think so as well. The cassowary exhibits I've seen have at least double that height. I see the fence at the back of the photo is much taller, interestingly enough.