Why is my finch restless, wing drooping, and sitting in its food bowl?

Restlessness, picking or pecking at body parts, and holding a limb (whether it be wing or leg) in an abnormal way can all be signs of pain or discomfort. Sitting in a food bowl may be a sign Alex just isn't feeling well enough to perch or doesn't feel like she can balance safely without falling. Having Alex examined by a veterinarian who specializes in birds is a good step toward figuring out what is causing her pain. Your vet may recommend radiographs to see whether there is something going on that would explain her unusual behavior. In the meantime I would keep all of Alex's food and water bowls on the bottom of her cage and lower her perches to almost the bottom of the cage so she doesn't hurt herself if she has trouble balancing or grasping the perch. It doesn't take much for these tiny finches to hurt themselves so creating a safe cage space until she can be examined is a good idea. I hope this is helpful. Good luck with Alex!