Why is my non-parent cockatiel on the nest and over-grooming?

The grey covering is a sheath that is on new or developing feathers. His skin looks irritated which may be due to parasites or infection. Ideally, he should be examined by your veterinarian or an experienced avian veterinarian. Clean and sanitize the cage, bowls, perches and toys. Discard anything that cannot be sanitized. Transition him to s commercial pelleted diet such as Harrison's, Lafeber, Exxact or Pretty Bird. You can supplement with a small amount of a fortified seed mix as well as with fresh vegetables and fruits.

If you mean just preening and grooming, then this is normal behavior. If you mean that your bird is pulling the feathers out, I would try to find the cause. Issues such as molting, where the old feathers are replaced by new, are normal. You will see pin feathers (new feathers poking through the skin that look like pins) if this is the case. If you aren't seeing new feathers, but are instead seeing redness, wounds, irritation, or "stuff" attached to the feather base, then this could indicate an issue such as parasites, infections, etc that should be checked out by a vet. In some cases, behavioral issues such as stress or boredom can lead to over grooming as well. Making sure Rio has an adequate diet, plenty of enrichment such as toys or treats he can play with, time spent with you, etc, and making sure his cage is in a stress-free and quiet area can help with behaviorally related feather plucking.

The other bird could indeed be preening her excessively. It is possible she could be starting a milt also. Monitor her for feather loss in other areas. Ideally, she should be examined by your veterinarian or an experienced avian vet to diagnose and treat any medical causes. If medical causes are ruled out, you will need to address behavioral causes such as stress or boredom. If the behavior persists and you confirm the other bird as the culprit, you may need to separate them temporarily. Don't worry, they can be caged next to one another. Feathers will grow back wrapped in a sheath. These are called pinfeathers. The sheath will be removed by preening and the feather will unfurl. You can bathe or mist them once or twice a week with warm water to promote preening and healthy plumage.

If the baby is old enough to be on his own, you may need to separate him to a different cage to avoid being picked on. Making sure he is eating and drinking and seems healthy is also a good idea as birds will sometimes pick on other birds that are ill or injured. Sometimes, parasites or even stress preening can cause a bird to overpluck feathers as well, so adding in enrichment such as fun toys or checking for signs of parasites may also help.

It is normal for captive birds to keep breeding even if they'd already laid a clutch, however if the male is harassing the female to the point where she's unable to lay on the eggs properly, or she seems stressed out, then separating them may be a good idea. If they seem OK, are eating and drinking normally, active, and able to sit on the eggs properly, then I would just keep an eye on them. it is a good idea to have some baby bird food and a syringe on hand in case the parents are unable to care for the babies. Young parents especially may have a harder time caring for their young, so stepping in with help may be needed.

If the chick is 3-5 weeks old, he can be removed from the cage. Use an appropriate hand feeding formula and feed 2-3 times daily. The formula should be warm (not hot) as most chicks will refuse cold food. He should also be kept warm. A cold chick will not eat. By 7-8 weeks, he should be eating seed, pellets and other foods on his own.

if you took the chicks away that early to begin hand-feeding and taming, having them where the parents can see/hear may help them calm down some. Otherwise, adding in some extra toys and treats for your female to interact with may help her a little. However, it may just take some time since she was busy caring for her babies and probably doesn't understand why they were taken away.