Skipper, the Paranoia Guy?
It sounds like a silly question. After all, Skipper makes wild speculations of Space Squids and robot clones, and has accused every member of his team of being a spy at some point. Even so, is it something else? We know that Manfredi and Johnson exist. And a Freeze-Frame Bonus in "Skipper Makes Perfect" shows that many of the wild things Skipper claims to have happened, HAVE happened. Is he really so paranoid if many of his accusations are based on real experiences?
Most paranoiacs prefer to isolate themselves, and feel powerless and depressed, which is a far cry from describing Skipper. He prepares, he plans, he leads, and he trusts his team during a mission, while a true paranoiac huddles in the corner with a tinfoil hat or raves alone in the street. He never deliberately isolates himself. Compare him to Buck Rotgut, who accuses others of being spies on the most trivial of reasons, and has no companions or long-term-plans.
While Skipper is certainly suspicion of bad things happening, and has trust issues, his fears have a basis in previous experience, and his confident leadership of the other penguins as he trains them to prepare for the worst-case scenario - which often happens - is a lot.
Rather than suffering from paranoid delusions, Skipper is more likely to be suffering from PTSD.
Kowalski, Sociopath or Narcissist?
Kowalski has been called both of these things, and it's true that he struggles to empathise and likes to think himself far superior to the other Penguins - to everybody, in fact. One important difference is the Narcissist's fragile, easily bruised ego, and another that they find the opinions of other people do matter. None of the criteria for narcissism demands they be shameless, dishonest, or treacherous. Some Narcissists value friendship highly - what better way to show you're the best, than having great friends? Who better to show you're rich, or talented, or fun, than your friends?
Above all the other penguins, Kowalski visibly preens whenever he's showing off, and more-so when he's right. Skipper even has a jar for pennies. In "It's About Time", three versions of Kowalski agree that they are really good looking. When Skipper is 'eating' Rico's brain, Kowalski is initially more offended himself, than concerned for Rico - but he still manages to feel concern for Rico as well.
Additionally, you're not the best if you cheat and lie your way to success. Narcissists may cheat and lie but then find their success is unsatisfying. Kowalski will do almost anything to be recognised as the best. But when he steals Mort's game chip to create his mind-reading device, the mind-reading device works perfectly, telling him how ashamed the others are of him. Despite being selfish and self-centered throughout the episode, their honest opinions matter much more to Kowalski than the invention, and he feels shame.
Kowalski is constantly inventing. Always showing off his latest inventions, his singing, his dance moves, his vocabulary. It's clear he believes he's the smartest, the best looking, the most skilled. The problem is that he also clearly feels a need to be even better than the best, even though he knows he's the best, such as in 'Brain Drain'. He's not perfect, of course. And when it shows that he's not... well, it hits pretty hard. When Kowalski fails, usually in the form of his inventions going wrong, he is utterly shattered. Sometimes it takes only the slightest imperfection to convince him of failure, with him considering giving up completely until his friends convince him otherwise.
Kowalski knows when he's failed - a sociopath will deny failure even when it is completely irrational to do so. He knows that the thoughts and feelings of others matter, at least those about him, while a sociopath doesn't care at all. He thinks he's the best but still wants to improve on that lead, while a sociopath thinks they already know everything and doesn't even try to learn.
Ultimately, while the two mental illnesses have their unpleasant similarities, Kowalski shows none of the shamelessness, violence and impulsiveness of a sociopath, and sometimes even suffers from his huge and yet cripplingly fragile ego, while the sociopath causes suffering while lacking the cognitive abilities to suffer emotionally as a consequence.
Rico, really a Psychopath?
You're probably going to feel great relief when I say that Skipper's terminology is way off in this case. Rico is not a Psychopath, at least not in psychiatric terms. Psychopaths, like sociopaths, have no empathy, no shame, no emotional ties, and no concern for any needs other than their own, the main difference being their lower intelligence and an even higher tendency for violence. Rico has shown all of these emotions on a regular basis. You can't factor his regurgitation skills into the diagnosis; it's a physical ability, and Rico up-chucks a wide range of useful things, not just explosives.
Rather than psychopathy, Rico shows more signs of Autism and Downs Syndrome. These are not just the expected low intelligence and poor verbal skills, but also his poor social skills and complete lack of impulse control. Even some of his physical features are linked to Downs Syndrome - squat stature, obesity, and a flatter face. In the episode "Needle Point", he uses the Speak-N-Spell to talk to humans to say some things. Autistic people who are non-verbal or partially verbal (like Rico) tend to use text-to-speech programs or "Let Me Talk" apps to communicate with others in a similar way.
Rico doesn't seem to make new friends as easily as the other penguins - his family is usually his social circle, and when he extends his social circle in "Stop Bugging Me", it is towards the friendly, easy-going Broaches who don't judge him on his intelligence or poor hygiene habits. And Rico passes no judgement on their habits either. Additionally, Rico seems fairly aware that Miss Perky is a lifeless doll. He's seen enough toys and adverts, and it's unlikely that he hears her speak, since he is so keen on getting a voice-chip for her. He's clearly offended when Marlene calls her a toy, while the penguins grab him and tell him that she just "doesn't understand". It's not really a social norm to focus your affections on a doll. But he still prefers Miss Perky to the smitten, slightly scary Shelley, whom he barely knows. It takes Marlene gently convincing him that a real person is better than a lifeless doll - which actually shows he trusts Marlene more than Shelley.
Rico also has a very specialised area of interest - high explosives. He's very imaginative in the way he uses them, and skilled as well. He doesn't blow things up to hurt people - he blows things up to see them blow up. Skipper shows great concern that Rico could as easily hurt himself as other people - why, in "Herring Impaired" he fires himself out of a torpedo cannon for fish! When he's suggested to have poor hygiene control, and shown eating rotting food and stuffing himself with candy until he's ill, it becomes clear that Rico doesn't just need to be kept under control; he needs somebody who will take care of him, because he can't really take care of himself.
Then there's his 'rampages'. Few mental illnesses are mutually exclusive. It's worth noting that despite his regular requests for "Ka-Boom?", when turned down by Skipper, Rico usually obeys, and he is usually in command of his own thoughts and actions. It is clarified in "Private And The Winky Factory" that Rico doesn't hear voices ("Rico don't talk to imaginary candy-wrapper people!"), which rules out schizophrenia; he probably suffers from Psychosis, with his episodes brought on by emotional stress. One time this is seen is in "Kaboom And Kabust", in which he is encouraged by King Julien to behave badly. Rico is pushed to choose between his family or his new friend, and Julien even describes himself as Rico's 'enabler'.
Private, the Sane Man?
Boy is Private adorably naive for somebody who's spent all their life training to be a Penguin Commando. But unlike Rico or Kowalski he's got no obvious social impairments. Despite having the tightly-knit penguins as his family, he's outgoing and friendly with everybody else as well. He seems possessed of average intelligence. His main character quirk (apart from being cute) is that he has some trust issues - he wants to trust just about everybody, sometimes to the point of mild absurdity.
The strangest thing is that there doesn't seem to be anything specific wrong with Private, despite his family and upbringing. Even his adorable naivete can be put down to cushioning from the other penguins.
Other possible disorders?
- Just like Rico above, it's possible that Kowalski may be displaying symptoms of high functioning autism/Asperger Syndrome (I write as a person with high functioning autism or Asperger Syndrome myself). A stereotypical portrayal of people with Asperger's is that they may be savants in their chosen field. Diagnosis as an Autistic doesn't demand constant nurse-maiding. Indeed, some on the Autistic Spectrum have genius-level I Qs. Now, let's look at symptoms of AS from TV Tropes' Useful Notes page and look at how they apply to Kowalski:
- Delays in social interaction: Kowalski doesn't have any friends outside of the other penguins and even then, he doesn't seem to be able to relate to the other penguins very much sometimes because of his logical way of looking at things and obsession with science. He straight up says in one episode he doesn't understand love and women and in another, he has problems with properly explaining to Rico how he feels about him when he is about to explode and can only gather up "I also love you in the same way expressed previously... dude."
- Logical Thinking: This is obvious - Kowalski is the most logical of the entire team and always thinks before he acts. However, this sometimes causes problems. In "The Hidden", he is so focused on thinking logically that he doesn't know how to react to things on instinct. He learns from this, however, but he is still the most logical of the group. He also doesn't understand why his teammates would choose the less logical path.
- Literal Thinking: This shows up less often, but it appears from time to time. For another example from "The Hidden", there's this quote from Kowalski: "Time to listen to that gut. Even though technically a gut cannot vocalize." He also took the phrase "sleeps with the fishes" seriously, noting that fish technically do not sleep, before realizing what the phrase actually meant and finally, when Skipper said that he doesn't know the meaning of the word surrender, Kowalski defined the word for him.
- Narrowly Defined Interests: SCIENCE! Kowalski loves to experiment, invent and talk about science, even if the person listening to him clearly isn't interested or doesn't know what he is talking about. This is where the Savant syndrome comes in - Kowalski is clearly the most intelligent one of the group when it comes to logical thinking, math and science, even if he is the second least physically capable member after Private and is quite socially awkward. While it's partly because he is very intelligent, Kowalski focuses so much of his free time ( and sometimes even work time, considering that he IS the team's strategist and analyst ) on science that he tends to forget to focus on anything else, gaining extensive knowledge of science and having only handful on friends, he is always happy to share his discoveries with his teammates, while forgetting that they aren't interested, leading him to get angry if they dismiss him.
- Speech Issues: While he is able to speak normally and even in a more sophisticated, intelligent manner than other penguins, he is very prone to Sesquipedalian Loquaciousness - using more complicated words when simpler ones could be used, which he is prone to even around his teammates, who have less defined vocabulary than him and may not understand what the words he is using mean.
- Motion and Motor Control: While this one's not that obvious, he is Skipper's second-in-command and yet he is, again, potrayed as terribly clumsy.
- Despite his problems when it comes to relating to other people, Kowalski is surprisingly sensitive and in touch with his own emotions, which is another trait a person with AS may have.
- He is sometimes shown talking to himself while thinking. Some people with ASD are prone to discussing topics with themselves if there's nobody else.
- There are times when he is shown having mood swings, emotional outbursts and sometimes he straight up loses his mind, especially if it's somehow related to his main interest - science.
- Taking into account that POM is a kid's cartoon, he shows two stereotypical traits associated with people with Asperger Syndrome - Insufferable Genius and No Sense of Humour. While the Insufferable Genius thing is simply caused by him being overly confident, most Aspies do get jokes, but the jokes they make are based around personal experiences or complicated wordplay, meaning there's ultimately no punchline.
- While Kowalski is capable of lying, he is usually honest. In fact, in an episode where he stole Mort's game, he tried to hide it from Private, only for him to get so frustrated that he just admitted to Private what he was hiding. And in another episode, he randomly revealed that he is irritated by the fact that Skipper is the leader despite being less intelligent than him after getting randomly worked up while explaining why Maurice may be plotting to overthrow Julien, which would be a pretty unpleasant surprise in real life, especially if that person was taught to be polite and keep certain thoughts to themselves.