My lovebird looks fat and swollen. Is this normal or a concern?

He does look a bit puffy, but it's hard to tell just from a few photos. Birds with full crops can sometimes have a "balloon" like appearance on their chest below their neck, that will gradually decrease as they digest food, and then fill up again as they eat, but it's usually not very visible in adult birds. However, as with any new pet, a general wellness exam with your vet is best to establish care, check for any issues, and treat them if needed. If Naoko seems in distress or ill at all, seeking care sooner is a good idea.

That does look concerning and should be checked out by a vet. Bulging of the stomach or near the vent could be any number of things including fatty deposits, growths or tumors, infections, or even an egg that is stuck and unable to pass. If she seems in distress, seeking veterinary care ASAP is best. Keeping her warm, eating, and drinking may help, however having it looked at is needed.

If the feather fluffing is only at night and the second bird is otherwise healthy, eating, and active I would not be too concerned, and adding a cage cover at night to keep the birds warm may help. However if it is fluffed up all the time, eating less, or showing other signs of illness, then I would schedule a vet visit and move the affected bird to a warm hospital cage to help it rest and rule out any more serious issues. The cage you have for both birds is also extremely small, so I would recommend placing them in a much larger cage that they can easily move around and stretch it and with some added toys to prevent stress and boredom.

Unfortunately, without an in person exam, it would be hard to say what exactly is going on. Egg-binding can definitely cause an obstruction and protrusion like pictured, as can issues with the vent being clogged with stool or underlying illness. If you suspect egg binding, you can try putting her in a warm water bath to help break up any stool crusted to her vent and to help the muscles to relax some to see if she can pass the egg. Since budgie eggs are so delicate I wouldn't recommend trying to remove it on your own as it can easily break inside her. Moving her to a hospital cage that is kept warm and with low perches/easy access to food can also help, as can catching her to help keep her vent clean and free of debris. I would also bring her back to a vet ASAP if the medication given is not helping.

If Bonnie is fluffed up, not eating or drinking and very listless it is likely that she may be ill or injured and veterinary care should be sought. if all your birds are affected, it is possible they are all ill from something contagious, or the cage may need to be moved to a warmer/less drafty spot to help keep them warm enough. Keeping them warm, eating and drinking, and separating any visibly ill birds to a hospital cage until they can receive care is best to prevent the spread of illness.

Thanks for reaching out about Kiki. Tail bobbing is a sign of difficulty breathing and should be seen by a veterinarian as soon as possible. Fluffed feathers can be an indication of attempting to trap heat. Ill birds in veterinary clinics are placing in heated incubators in the 85-90 F range to provide support, so giving supplemental heat can be helpful. This bird is probably very serious and early veterinary intervention can improve recovery. Good luck.

You can monitor Cloud for additional symptoms (lethargy, loss of appetite, bleeding, etc) or you can have him examined by your veterinarian or an experienced avian vet. If you can post an image with a new question, we may be able to provide more specific advice.