For # 5 I'm going to guess

>!Super Smash Bros Brawl

The game has more than one name.

>!SSB, SSB Melee, SSB Ultimate, etc

The king who rules over this whole storybook,

>!Tabuu is the main hidden enemy ruling in the Subspace Emissary (Single-player storyline part of game). He is subspace and creates an army to take over everything.  

He has more than just one look.

>!Tabuu can grow into a large size, can transform to have wings, can transform himself into a gold cage or giant blade. 

His kingdom he rules over with his hand,

>!In the Subspace Emissary, Tabuu controlled the Master Hand and used it as a mouthpiece to call the shots of the take-over. Directing and leading Bowser, Ganondorf, Wario and other villains through Master Hand. 

From the computers to a pyramid land.

>!There's a desert area and robot/computer area in the Subspace Emissary.

The king has the power of fire, like A Zone.

>!The Flat Zone is a stage and it has parts that can burn you. The main character for that stage (Mr. Game and Watch) also has a move that can burn you. Tabuu has moves that cause explosions, fire bursting out when it hits, which can burn you. 

And yet, he was banished to live alone.

>!Tabuu is the embodiment of subspace and therefor cannot leave subspace. Nothing lives there, so he created a spectral army to turn people of the world into trophies and bring them into subspace. 

A world in this tale has many sweets,

>!In the subspace emissary, there are areas that have Poppants, which are enemies that drop candy as they run away. These candies can be consumed and will heal you. 

But the desert still has many treats.

>!The desert area has hidden areas where special trophies and extra un-lockable characters can be found. 

This game has plenty references to others from the same company,

>!SSB has a cast of characters from Mario, Zelda, Pokemon, etc.