I think they can definitely feel distress or suffering. I think some chewing of feathers can be due to boredom and sheer habit.
I would consider having a sort of hanging gym that he can hang out on when he's outside of his cage and load it with toys that HE finds interesting. Example, foraging toys, preening toys, puzzles, mechanical toys etc. I think it's important to provide as much distraction and stimulation as possible.
I don't think that housing him in the same cage as the sun is safe even if they do get along and I know some parrot owners leave their parrot out of their cage 24 hours a day but frankly I don't think it's a good idea at all. I think you're just going to have to try all kinds of different things until you find something that works for Beau.