Timber sleeps in his cage, on the highest perch in the cage. I don't know anything about the "Bird Nest" you mention. First thought would be that you don't want to encourage nesting behavior because even unpaired females can lay eggs, leading to calcium deficiencies, being egg bound etc. As I said though, I don't know anything about the item you are talking about.
Hi Akka! Welcome!
All of my greys as well as my macaws are going through their molts, too. Just vacuumed up a lot of floofies!
Would love to see a pic of Blu!