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You're speaking to Dr. Michael Salkin. Welcome to JustAnswer. I'm currently typing up my reply. Please be patient. This may take a few minutes.
I'm sorry that your question wasn't answered in a timely manner. We don't have many avian vets on this site. Regrettably, your conure's symptoms are important but they're not pathognomonic (specifically indicative) of any one particular disorder. Perhaps most important, your conure is at life expectancy (15-25 years) and so there's likely to be more than one thing going on at this time.
Feather loss on the head may be due to aging, hypothyroidism, bacterial and fungal infections. Shaking of the head is a nonspecific sign of pruritis (itchiness) or perhaps pain. Partly closed eyes indicates an ill bird but not the cause of the illness. Problem flying suggests weakness but, once again, not the cause of the weakness.
It's important to note that once a conure acts ill it's already quite ill and in need of the attention of an avian-oriented vet (please see here: www.aav.org). This is a protective mechanism because sick birds are attacked by other birds in the wild and within their flock. An avian-oriented vet might first treat symptomatically and supportively by providing supplemental fluids and electrolytes by needle and tube feeding a "recovery" food. Blood tests and cultures of your conure's choana - the slit between its oral cavity and nose - and cloaca (vent) may be taken. Whole body X-rays can be quite helpful as well.
Nutritional imbalances are common in our pet birds. What has your conure been eating, please?
That's an excellent diet and so malnutrion shouldn't be incriminated in his malaise. Please continue our conversation if you wish.
I can't rule that out but without knowing the cause of the parotlet's condition that must remain conjecture.
Ectoparasites that are susceptible to Scatt are rarely an issue in a 21 year old with no exposure to new birds. The antibiotics in Amtyl are reasonable as broad spectrum presumptive therapy when a bacterial infection is suspected. I rarely rely on antibiotics in the water, however, because most ill birds don't drink enough to medicate themselves properly. Colloidal silver has no scholarly studies behind it in birds for me to be able to recommend its use.