Medaka Box/WMG

Kumagawa's abnormality isn't healing
Much like the ex-presidents invisability, healing is a side effect of his true, terrible abnormality. I have no idea what that is but I do know that it is terrible because Medaka already has it. That was what Oudo found when he tried to use his Unreasonable Taxation on her. Just like whenever Kumagawa attacks someone, his arm was horribly damaged, then instantly repaired, the only real damage mental. She obtained it three years ago when they last met, perfected it, then realized the utter wrongness of it and immedietly repressed it.
 * Confirmed.
 * In chapter 70 he downright states that his power could destroy the world, if he doesn´t pay attention.

Kumagawa is actually a Split Personality of Zenkichi
No real reason, really. It would just be hilarious if her biggest follower and the one guy she couldn't help/control were the same person.

Kumagawa is reformed and will become the Vice President INSTEAD of Zenkichi being promoted

 * Kumagawa will also win Medaka's heart. Zenkichi will become an Unlucky Childhood Friend. At least he has the miser for backup.
 * Confirmed, by chapter 92. Well, the part about Kumabawa becoming Vice President, anyway. No news about the other part yet.
 * Could possibly be Zenkichi's reason for wanting Kumagawa's arm band.

Medaka is a Humanoid Abomination / Cosmic Horror in a human shell
After what was revealed about Medaka's inner self in chapter 55 and the severe Creepy Child vibes she had in the flashback, it is reasonable to think that she's something else playing at being human with varying success. It'd explain her God Mode Sue ability to bend reality (Tropes Are Not Bad). Whether she actively knows this is another matter. "Medaka (Chapter 55):Within a beast like me in an abnormality that a human cannot withstand."


 * Well, "Kurokami" means "Dark God"!

Zenkichi is a Normal
One that is so Normal he can deal with the sheer insanity of all of the Abnormals and Minuses running around, which manifests as his willingness to befriend them as equals and apparent resistance to certain abilities. Or maybe it's because he's been hanging around Medaka, an Abnormal compared to other Abnormals, for so long that everything else is easy to deal with by comparison.
 * Think about the number line. The Abnormals are the super positive, while the Minuses are the super negative. Right smack in the middle of them? Yeah, Zenkichi could be the zero, neither positive nor negative. (Ok, that sounded better in my head.)
 * I agree with you on the 'Normal' part. But he is not right smack Normal. I'm more of the opinion that he is a 'special' Normal, in that he is BOTH super positive and super negative at the same time, leading to others thinking/feeling that he is a 'Normal'. Otherwise, its kind of hard to explain the door incident when it switched back to his DOB when he tried to enter...
 * Further expansion of this theory is that he could keep up with Medaka's power leveling, be one of the first to meet the minuses, etc. Why is that so? Either he has abnormal luck, in which case, he would be list either an abnormal or a minus, or he's what I'm guessing: At the same time an Abnormal and a Minus, so everyone can only understand him as a Normal, when he is actually Normal, because he is 'Abnormal/Minus' to the extreme.
 * How exactly is he an Abnormal and a Minus at the same time, though? Especially since being a Minus/Abnormal seems to depend a lot on personality. For example, Munakata's power is basically the urge to kill, which is technically a minus, yet he's an Abnormal. Kumagawa can heal, but he's so damn evil he's a Minus. How does Zenkichi emulate superpositive and supernegative at the same time?

Zenkichi is a Zero.
Based on the math theory going on -- the Mary Sues are "13", the Anti Sues are "-13"... and Zenkichi has shown he's more or less immune to both's abnormalities. Following the math, this would make Zenkichi a Zero -- a null.
 * He may be a "neutral", in that he neutralizes abnormal powers. He might even be able to touch Mukae's hand without it rotting him.

Someone else gave Kumagawa his "All-fiction" Minus
It's been confirmed that Kumagawa didn't have that power when Medaka beat the crap out of him in middle school. It's possible someone else gave him the ability a few years ago, and is the real Big Bad of the series. The idea of someone running around creating Anti Sues with the power to destroy the world For the Evulz is pretty creepy.
 * Confirmed. It was Ajimi.

Zenkich has Anti-Magic
There are a few hints that Zenkichi may not quite be the Normal that he seems, and that his abnormality may be the ability to resist/keep up with some Abnormals. He's certainly been shown to resist a lot of powers, it takes a combat abnormality or a natural phenomenon (explosions, poison gas, etc.) to take him out, usually. He even resists syringes made by an abnormal when fighting Medaka II!
 * And he can remember Hinokage!
 * Fridge Brilliance: Why can Zenkichi fight back against Oudo's body control command to kneel, despite being a Badass Normal? He's a Zero -- an anti-abnormal, of course. How can Medaka do the same thing? She copied Zenkichi's abnormality, of course. How is Medaka going to fight against the -13 class? With the same powers, of course.

Zenkichi's original ability was Live Zero
Going on the above theories, and the name of one of Ajimu's skills. Maybe Zenkichi's original ability was Live Zero?

Ajimi is a personification of the Void
Yeah, there is another one!

Zenkichi is a Youkai
All of the youkai in Nurarihyon no Mago have the same two colored hair that Zenkichi does, so maybe his ridiculous ability to not die comes not from hard work, but from being a youkai. I mean, what Normal could survive being impaled in the back by seven or eight weapons?

Shiranui is an Emotion Eater
This page states that she "swallows" people. This might be hinting to her ability to eat emotions especially negative emotions since she also states that Zenkichi is too sweet to swallow. There is also the Big Eater aspect of her character.
 * Chapter 85 reveals the name of Shiranui's abnormality is "Real Eater", the actual effects of her "eating" Hinokage has yet to be determined.
 * Add this theory with how it's said that the personality shapes the ability, considering how Hinokage's Mister Unknown becomes Theme Song, maybe her skill can manipulate somebody such that the skill would change.
 * Well actually, it seems to run in the family. She can, in a similar way to Ajimu, trade someone's ability with another one.

The actual Medaka is a dream and the dreamer is Zenkichi.
Idea behind this is the meaning of the Magical Girlfriend trope. The Magical Girlfriend is basically an imaginary friend, who are often more "perfect" than the child, who creates them, and always leading the child into new adventures, like Medaka did with the young Zenkichi.

When Zenkichi and Medaka met each other the first time, Medaka possessed no personality and Zenkichi was in an age, where children start to create this imaginary friends. Somehow, Medaka adopted Zenkichi´s idea of his "perfect" friend and became it! This is why Medaka is so idealistic: She is an ideal herself, a personification of Zenkichi´s own dreams as child. While Zenkichi grew up and start to saw the flaws of his ideals (and became a little cynic), Medaka kept her sometimes childish naive personality. Still, she is dependent on Zenkichi, as we see by her complete breakdown, whenever Zenkichi was close to death.

That´s said, it is not Zenkichi, who protects Medaka´s ideals. MEDAKA is the true guardian, always trying to uphold the ideals, even Zenkichi became to doubt, which allows Zenkichi to develop an realistic, but still optimistic view on the world.

Gagamaru didn't always have Encounter
During the fight with Shibuki, when she uses her Scar Dead on everyone, Gagamaru is hurt too. With his ability, though, he should never have gotten hurt in his life. Therefore, in his childhood, he must not have had Encounter yet and it may have developed from his desire to push away all of the "unexpected accidents" in his life.
 * He actually did have Encounter when he was a kid - at least, by the time he met Shibuki.
 * He probably did always have it, it just wasn't developed enough yet for him to control.

Ajimi
will become the next Big Bad.
 * could possibly be the current Bigger Bad

Ajimi is Lonely at the Top
Her entire motivation for starting the Flask Plan in the first place may have been simply to create other beings on her level.

Ajimi is a Humanoid Abomination

 * Similar to the WMG involving Medaka. Ajimi has the Orange and Blue Morality for a eldritch horror. But unlike Medaka in the WMG she is not benevolent.

Zenkichi will spend the rest of the arc trying to decipher the cryptogram

 * Since he is kind of a Butt Monkey, and there's been some lack of focus on him
 * Confirmed as of Chapter 115.

Zenkichi actually has an Abnormality/Minus, and Ajimu traded Parasite Seeing for it with Lip-Service

 * She had to trade All-Fiction to give Kumagawa his Book-Maker back, so presumably she can't just give other people skills as she wishes and can only swap skills. She has Zenkichi's original ability now and perhaps this would become integral to the plot later on.

Whether you would develop an Abnormality/Minus depends on your blood type.

 * That, or the author REALLY likes the AB blood type, even by Japan's blood type-obsession standards.
 * It's probably because any other blood type is too "Normal" for most of the characters.

There is a more serious reason for Zenkichi being more cynical in the present

 * Zenkichi as a child generally seemed extremely cheerful and optimistic. While you could dismiss it as simple maturity, he still seems to advocate the ideals that he once gave to Medaka. Knowing Isin, it may connect with this current

Everything since the first genre shift has been an elaborate plan by the author

 * Not necessarily in the "meticulously plans out the entire plot" way, but more in a "what? My story's not doing so well so I should change the genre? Fuck you, I'll show you genre change" way.
 * The first part is simple enough: take the original premise, file off the romance subplot into standard characterization and then apply Medaka's sheer ridiculousness to the typical fight arc.
 * Part Deux: Deconstruct/subvert/parody the shit out of that change. It's not just a shonen/fighting manga: it's a shonen/fighting manga where the main plot is to make people into shonen/fighting characters. Don't give then special abilities through "devil fruit" or "soul reaper/hollow/full bring" or "ninja magics" inherent to the setting: straight up call them "Specials" or "Abnormalities."
 * Part Tres: Just keep at it, raking in both that sweet, sweet shonen fandom and those who enjoy a good vicious parody, and everyone in between.
 * Part Shi: Here's the pay off. After all of this, after introducing the most mind bendingly broken character yet (to be certain, give her quadrillions of abilities), after going this far... flat out say the entire journey up to this point has been worthless. No one grew. No one achieved anything. But now that the characters know this, they can progress. You know what's really important now? What'll finally get everyone to where they need to be?
 * That goddamn romance subplot you dumped way back at the beginning. Fighting? Who needs it, the main heroine can never be beaten. Making friends? They're already friends, and no one's actually really trying to antagonize anyone. No, what needs to be address is the UST in the main characters. And it'll be address in the most over the top, deconstructionist/reconstructionist/weirdest way you can pull off, capping off a truly ridiculous series.
 * This, my friends and fellow tropers, is Nisio Isin's grand plan to screw with everyone. It does not necessarily need to be maliciously based. Hell, it could have even been planned from the beginning. But the important part is outlined above: turn a typical shonen tale into a twist, non-ecludian mess. Ouroboros that thing up. It's a slice of life/romance, then battling, then a parody, then a deconstruction, then a reconstruction. Finally, it's a romance arc again. And always, always, make it self aware and ridiculous.
 * Part Five: Profit.
 * I applaud you sir. I had a similar theory, but your explination sounds better.
 * This seems to be a theme in Nisio's works. Bakemonogatari, Katanagatari...fighting is ultimately meaningless in them too.

Sukinasaki is going to be the final villain to be effectively beaten in Shonen-style, and Najimu Ajimi will end up being The Unfought

 * Seems like that.Sukinasaki is a downright Creepy Child who has proved to be somewhat evil and manipulative in the One Shot already, and seems to be an old enemy to Kumagawa himself, who was, by the time they met, the pre-Big Bad. Would that make her a Bigger Bad character? Well, about this, I don't know. Also, she's got a quite broken Abnormality, as she can brainwash and control everyone by using her cards(except, of course, Medaka and Najimu).
 * As for the Big Bad Najimu Ajimi, well, let's see... Immortal?Check. Has an overwhelming number of different powers?Check. Can negate her enemies abilities?Check. Can read other people's minds?Check. Can be anywhere, anytime? Check....In the end, Najimu is one of the most evident game breakers in manga history, possibly. There's no possible way she can be defeated in a battle against the characters, except maybe for Medaka, as she already mentioned(although this can simply be Dangerously Genre Savvy). As a matter of comparation, Kumagawa was able to erase the world with his ability, and couldn't beat her. The best he ever could do was to seal her powers, an act that has been apparently losing its effectiveness...This way, she's going either to change her ways and leave the main cast alone(which can really happen, if Medaka bests her both in arguments, or in the election), or win, and then in a would-be quite spectacular twist, resign from her victory, and leave. But battle-wise, she's physically invincible.
 * Partly Jossed, as Sukinasaki is revealed to be quite a nice individual by the end of her chapters, completely averting the image of Manipulative Bastard she has created in the one shot.

Najimu Ajimi is the Author Avatar of Nisio
The Sheer amount of fourth wall breaking on her part, and the implications that the entire plot is a product of her imagination turned into reality very strongly suggests that Najimi is both the Author Avatar and a Self-insert genderbended version of Nisio himself.