Can't thank you enough for all the advice and attention you're giving to a beginner bird owner, this is truly helping so much! I was thinking that in case the perches are indeed too thick, I could split some and sand them down nicely, to fashion them into the right size. The perch you mention isn't really a twig, as in reality it's way thinner than on the photo. It's a flatter kind of perch that kind of goes up (store bought, so that's not something I picked up from outside). I'll be replacing all the clips the toys hang from with twine, and will be adding a ladder. Thank you again!
About the rope toy, I was thinking of cutting off the fibers, do you think that would work?