Boredom in caged birds can lead to a variety of behavior problems, feather pulling and self-mutilation being common and excessive vocalization, especially when alone and lonely. Try to provide your birds with more freedom and novel objects to manipulate and investigate. Leaving a radio or TV on when you leave them alone may also help enrich their environment. Same for dogs and cats, whose human companions are away at work all day. So I advise you to train the cat to either jump over or crawl under the expandable gate to get to her litter box.
Cats like to have the litter box located in a quiet, low-traffic area of the house.
You may want to consider allowing your cat to eat on a kitchen counter where the dog cannot reach her food. Eventually your young dog should grow out of her desire to snack from the litter box. But the cat food will always be a temptation. He intentionally puts his treats in front of her and growls at her. It is amazing how some dogs become bullies, just like some children.