My handwave for a bunch of things. About five minutes of vigorous palm motion.
The island is a floating island. There're a lot of them in fantasy, but it doesn't really matter how it floats so much as that its "natural state" is floating*.
A long time ago: Ballos goes completely nuts. He tries to kill everyone.
Jenka decides that's a bad idea, so she tries to isolate him, teleporting him to the floating island. Ballos, having no teleportation ability of his own (it would have shown up when you fought him) decides to kill everyone and free himself by causing the island to crash to the ground. Jenka counters this by making the core, which has the ability to screw with gravity and acts as a seal on Ballos' power. The water in the core's room acts as a gravitational sink - it can be raised or lowered in order to offset any fluctuations in the power struggle.
Slightly less of a long time ago: Misery decides that all that crazy powerful magic shouldn't go to waste. She approaches Ballos and gets him to make the Demon Crown, which would let the wearer use some of Ballos' intense magical powers. Like any story with an evil genie, he grants her wish, but gives it a nasty twist. She is bound to forever serve the master of the crown, and every time the crown is used it acts as a corrupting influence since Ballos hates everything. This creates all sorts of nasty stuff as time goes on, such as the red flowers, spikes, et cetra. All of hell (since it's closest to Ballos it would logically have more corruption), and almost anything red and evil can be attributed to this.
Ten-fifteen years before the game: Some scientists (Responsible for most of the modern influences upon the island. Probably including Malco and the power room) find the core. They see a fluctuating water level and are all "Sweet! Free energy!"**. They build platforms in the room for observation or something.*** Some killer robots come through and try to destroy the base (presumably since the scientists are from another country). They attack the core since it's central to the power generation operation, and get wiped out.
Later on: Quote kills the core. Ballos is now free to try to kill everyone. He starts stage one of his plan, bringing the island crashing to the ground. When Quote and Curly kill Ballos, he isn't adding any extra downward acceleration anymore, so the island stops falling. Incidentally, since Ballos is spending a vast amount of energy pulling the island down he isn't fighting at his full "destroy a city in one instant" capacity.
*The game says Jenka confined Ballos to a floating island. It doesn't say she confined him to an island and then made it float.
**Vaguely Supported by the music track being called "geothermal"
***The core would be virtually unbeatable if those platforms weren't there to let you dodge the shots. I assume that Jenka originally had it in a platformless flooded cave, which would make it much better at protecting itself
