In order to acquire all of the Chaos Emeralds in the game, you must race a character named Johny multiple times, winning the races. Here are the seven locations you can find him in:

Northeast of Haunted Ship

Northeast of Southern Island

Northwest of Machine Labyrinth

Northwest of Plant Kingdom

Southeast of Machine Labyrinth

Southeast of Southern Island

Southwest of Sky Babylon

To unlock Blaze as a playable character, beat the boss of World 3 (Coral Cave).

You can find a koala playing a guitar on Windmill Island after beating the boss in Big Swell. By speaking with him, you can listen to all of the in-game music and dialogue, as well as more missions that will unlock music that would otherwise be unattainable.

To unlock a new ending in the game, you must acquire all Chaos and Sol Emeralds in the game.