Katamari Damacy/WMG

The katamari is actually a gravity amplifier
That's why it can only stick small objects first and then larger objects later! It makes each of the gravitational strength of the things stuck on it larger.

The Hoshino mother didn't believe Mutsuo and Michiru for reasons other than their being little children
Mutsuo: In WLK, Mustuo is forgetful. He probably has ADHD or something, and so Mizue probably ignores anything he says.

Michiru: Mizue probably mistakes Michiru's sixth sense for a bad case of paranoia, and so Michiru is ignored as well.
 * Also Michiru doesn't actually say anything at all until the very last cutscene expet for the "I feel the cosmos!" parts, which because she flies of into space in them, I don't really think they're really happening in the plot. Something about the way Mutsuo talks doesn't really feel like he's all together in the head. So his mother could be writing it off as a delusion while its really happening. Maybe if Michiru wasn't a mute she might listen.

When The Prince has a son, he will be named "The Duke of All Cosmos"
Simple logic. The Emperor begat the King who begat the Prince. Each generation is moving down one noble title. Something BIG will happen when they run out of noble titles. Possibly infertility; possibly the Big Crunch.
 * The Emperor was pretty old looking; perhaps age is involved in the title. Once the King gets old, he'll be renamed the Emperor; and once he kicks the bucket, the Prince shall become the new King.
 * We see a young King in We<3 Katamari, though; as far as we can tell, he's still the King, even as a child.

The Katamari is Government
The Katamari starts out small but gradually becomes bigger, consuming everything it meets, growing exponentially bigger, eventually consuming people, buildings and entire countries. People do not care about the Katamari until it personally is a threat to them, ignoring it, even as it destroys everything around them; but once it is a threat to them, they cower in fear, or try to shoot it if they have a gun, but to no avail.
 * To top it all off, who caused the problem in the first place? The King of All Cosmos. A lot most of the issues the government fights are self-created.
 * And without it, something vitally important to the continued function of the world would be lost! It fits perfectly!

The game makes perfect sense.
All because The King is drunk or insane during the entire thing. Starting off is the whole drunken bender thing, but he doesn't recover. When he sends the Prince to Earth to roll up the katamaris, he takes regular household objects and clones them, places them all over the area, and perhaps even makes them move- to help train the Prince. The Prince, the katamari, and the objects are all invisible, which is why no one notices them. Also, the King is too drunk or crazy to realize he could just create the stars again...

But it all makes sense!

Also, yes. I'm on some good stuff. No, you can't have any.

The Great Cosmos is a Fisher Kingdom.
All the insanity and surreality is due to the fact that the King Of All Cosmos is a Cloudcuckoolander with reality warping abilities. (This is a trait their whole extended family shares, which is why it always rains whereever June goes, Jungle has Visible Invisibility, and so on. The King's is just the most powerful/has the most effect.) Presumably, things weren't so wild when his stricter and straight-laced father was in charge; once he handed down the crown, however, the whole universe fell under the King's sway, and Hilarity Ensued.
 * This is also why the Prince can revisit areas he's already rolled up and find everything restored: the King restores everything to normal after turning the katamari into a planet/constellation/stardust/whathaveyou. Otherwise, they would've run out of resources long ago (or, y'know, completely destroyed Earth by rolling it all up). This may be entirely unconsicious on his part, or he's using Obfuscating Stupidity and doing all this for his own amusement/to build the Prince's and Cousins' character/because Katamari turned out to be popular.

Havana is a midget.
And also just a few years younger than the King. It's been shown that cousins whose heads are shaped similar to the Prince's become flat on the sides and a bit more elaborately colored when they mature. And that's exactly what happened to Havana in WLK.

The cousins are all heirs to control over sections of the Cosmos.
The cousins are actually all destined to become kings and queens of parts of the cosmos. For example, since Kuro loves anime, he will become the King of All Japanese Cosmos, or the ruler of everything Japanese in the cosmos. And since Sherman's a snowman, he'll become the King of All Cold Cosmos, or the ruler of everything cold in the cosmos.

The Royal Parents of all the Cousins restore everything back to normal after each level.
If all of the cousins are heirs to different parts of the Cosmos, then their parents must be the current rulers of those respective areas, right? So, building off of that, they're the reason you can keep revisiting areas and the world hasn't been completely destroyed yet: whenever you finish rolling a katamari and leave the area, they use their powers to restore everything. Since they all have their own areas of expertise, by working together, it takes them only about as much time as it takes the King to finish putting the latest Katamari into the sky.

Their children, meanwhile, are just starting to learn or hone their powers; they all have natural ability, but not much control. (Given the nature of Katamari, it's likely some of them have weak-seeming or eccentric talents; for instance, June may have budding Weather Control, compared to Opeo possibly being the patron of Woobies and Chew Toys.) Katamari-rolling is part of their training, as it teaches patience, good judgment and self-control. (Besides, it's fun.)
 * I agree with both of these completely.

Nutsuo isn't a real cousin.
He's really Mutsuo Hoshino in disguise. Think about it, Mutsuo and Nutsuo are only one letter/character away from eachother. This is also why Nutsuo's arms are so low down. Mutsuo's head is in Nutsuo's neck. As for how the two can exist at the same time, well, the Katamari universe frequently violates common sense and the laws of physics.

Everyone in the games exists.
We just don't know where they are yet. What? This IS Wild Mass Guessing.
 * Except whoever made the game knows. As for why no one remember's being rolled up in a Katamari? Same reason you can replay the levels in the game and everything is back to normal.

The sumo wrestler is an Abzorbaloff.
Based on the fact that rolled-up objects just seem to merge inside his body...

The RoboKing's confidence problems come from his creator.
In other words, he reflects the Prince's own insecurities about eventually taking over for his father. When the King is knocked unconscious in Katamari Forever, the Prince doesn't feel even remotely ready to take over managing the Great Cosmos, hence his scrambling to create any sort of substitute. These feelings of anxiety, inferiority and angst were unintentionally transferred to the RoboKing's core when he creates it, resulting in his neurotic personality.

The King wasn't just upset at being 'replaced' by the RoboKing.
He was also disappointed the Prince hadn't risen to the occasion and stepped up to manage the Great Cosmos while he was knocked out. He saw the RoboKing as nothing more than a crutch his cowardly son had cobbled together, and that only further fueled his outrage. Rather than lashing out at his son, however, he had a 'safer' target in the RoboKing himself.