Welcome to the perch.
If you already have an avian veterinarian great if not please get one and make an appointment for your cockatoo and any cockatiel(s) you have.
An exam is not painful to any parrot and is just that, an examination. The vet will weigh the parrot, look at the eyes, nares (nostrils), ears, listen to the heart with a stethoscope, look at the vent, feet, legs, have the parrot grip onto fingers or perch on arm to determine strength, look at feathers and then review, do a history of the bird's current diet, care, caging and address any concerns you may have with the parrot's health. Ask the vet about the dry feet, the prior diet and the behavior.
Collaboration with a qualified, experienced avian veterinarian is the most important relationship you can have for the health of your parrot. It's very tough to provide online suggestions over suspected health concerns. Generalizatons are great and sometimes true but not always correct. Dry feet can be a reaction to dry heated indoor air in winter or the symptom of an interal med. issue, only a vet can tell.
Suspected emaciation alone is reason for a trip to the vet. Parrots can have diabetes and other metabolic issues also not just humans. Only a vet can give you solid answers. All we can do is give you general answers as pertains to care.
Since you are a newbie at being u2 mommy what you think is dry feet could be or not, what you think is underweight could be but the cause could not be from the prior diet, or could be, only a qualified, experienced avian veterinarian can determine all of this.
The dry skin could be from low humidity in your home or from a thyroid issue or both or dozens of other potential causes. The weight could be from being underfed or poorly fed before you or parasites from poor hygiene in a home prior to you, or both, as an age 25 cockatoo could have had many homes before you.
Please have your Too and any Tiel(s) examined by a vet. and let us know how it goes.