Cody thank you so much for your kind reply. The nest box came with the cage so I didn't know that it should not be in the cage. I will remove it thanks for the guidance.
About the cage, the lenghth is 1.5 feet while the width is about 2 feet. The birds are bought a few days ago so I don't know about the age but the yellow budgie has brownish nose color while the green pair has purpulish colored nose, if this is helpful in determining the age...
Before this the yellow was in another cage with no nest box and she was scratching the bottom of cage and doing the same side to side movement and she is doing the same while sitting on the nest box opening. What is meant by this behavior?