What about mixing avian species?

Don't know but I'll give you a bump in case someone else does.

 

What kind of parrot?

The first problem I see is your hardware cloth. The beaks of some parrots are strong enough to chew right through that stuff. And unlike chickens, parrots will climb on the wire using their beaks and can die from the zinc in galvanized wire. Chewing could be an issue on the plywood, too.

I lot depends on the temperament of your particular species of parrot and your breeds of chickens. If either one is aggressive, you could run into problems.

Here's a great forum for people who build outdoor housing for their parrots. You might be able to get some good ideas there, too.

http://naturalbird.com/

 

Not a good idea. Not only for the reasons posted above (that apply to parakeets as much as they do parrots) but because exotic birds can carry diseases that do not affect them, but that can kills chickens and a number of avian diseases are transferable from the chickens to the exotic birds as well.