Some of these are rare.
Neurofibromatosis is a medical condition where a pookie's body blisters into scars, or the pookie's face hangs to a side. It is not contagious, but it's rare.
Exterminavitbeasta is pronounced Ehx-tir-men-ahv-it-beest-ah. Its common name is "Animalitis" since most people can't pronounce it. It is when a pookie watches so much of an animal show (Teddy Town, Bunny Barn, etc) that they start acting like that animal.
Conjoined Twin Pookies
This is super rare in Club Penguin. It is when two pookies are joined together at the hips, sternum, buttocks, etc. or held by a piece of cartilage together. Sometimes they'll be able to be taken apart, but sometimes they'll be joined for life.
When two twins roleplay as conjoined twins, they will sit together and follow each other everywhere. Sometimes the twins will die from infection, illnesses or tuberculosis. This is not always the case.
ADHD stands for "Attention Definition Hyperactivity Disorder". It is a neurodevelopmental and mental disorder in which there is problems paying attention, excessive activity, or difficulty controlling behavior which is not appropriate for a penguin's age. These symptoms begin by age six to twelve and persist for more than six months. It is not very serious.
SIDS is short for "Sudden Infant Death Syndrome". It is extremely rare, but can happen. It mainly occurs during sleep, and there is no sign of struggle or noise during the condition. Bed-sharing, smoking, side-sleeping, and blankets that cover their arms and body increase the risk. It is currently rather unknown, although 80% of infant deaths are caused by it. It is common on CPPSes though because the word "dead" is allowed.
Pica is a disorder where a pookie/middle/biggy has a desire to eat something that is not food, like a chair, tissue papers and dirt. This can cause extreme worry to the fam fam. A sign is when a member of the fam fam says something like "eats chair".