I don't cut up anything I give the chooks. They just pick little pieces off everything. It's surprising how much they can get through and what they can demolish. They are like little eating machines.
As for bugs, I remember one day Marcy found a cockroach and Grace was chasing her around really enthusiastically trying to get it. Usually Marcy does what Marcy wants, but Grace was motivated to try to get that "yummy" (yerrghh) bug off her. It was a "prize" (again, yerrrghh).
I had some nice bits of tree branch that I got the loppers to leave when I had my big tree pruned last time. I was going to make a parrot stand or perch, but they've just been lying about. I've put them in the open run. The little little girls stand up on them. They look so cute. It makes the open run look a bit less like a prison yard as well.