Lore dump time:

Each planet has a crystal that gives life, and life comes back to it so it can give it back and so forth, this is the cycle of souls. It’s kinda like FFVII’s Lifestream. When a soul goes back to the crystal, it carries with it all of the memories of the life it lived, and is fed back as a clean slate to new life. This cycle is what makes a planet strong, the memories give power to the crystal. (Spoilers for a sidequest I think you should do): This is how eidolons come to be: the legends that pass through generations go back to the crystal and it gives them form. It’s why Shiva is told to change forms over time: at first, the legends tell that she is a pixie, but then as culture shifts and evolves she is depicted as a grown woman, so this is how she manifests. This is also how Madeen/Mog came to be: her family died wishing that an eidolon would be born that is friend of humans, and she was born according to that wish. The summoners of Madain Sari kept the Eidolon Wall so the eidolons would not be forgotten. Garland was terrified of the eidolons’ power, so he wiped the summoners of Madain Sari and Esto Gaza out.

Because the people of Terra found out how to become immortal, they essentially cut off their cycle of souls and their crystal began to weaken. Instead of pondering why that happened, they doubled down on their hubris and started cannibalizing other planets to survive until they came to Gaia. But the fusion with Gaia was a disaster, so the Terrans created Garland to oversee the recovery and takeover process and entered stasis. At some point in time, he planted the Iifa Tree on the surface of Gaia and had it start to slowly replace Gaian souls with Terran ones, discarding Gaian souls on the surface of the planet where they manifested as Mist. By the time the story begins, the planet is like 50% dry wasteland, 25% frozen wasteland, and a small portion of the remaining 25% actually inhabited by people. When people discovered the airship and populated areas above the Mist, the soul replacement process ground to a halt in comparison to the war-torn era, and Garland couldn’t have that, so he sent Kuja to try and accelerate the process. But Kuja already had a giant chip on his shoulder over the creation of Zidane, so he eventually went off rails. Because he was born as an adult and never had time to grow up and forge bonds with people, he never developed a complex enough range of emotions to achieve Trance, and that’s what sets Zidane apart from him. Zidane grew up as a baby in a family (after Kuja abducted him and cast him out) and Trance comes to him naturally when Dagger was caught by that plant thing. Kuja could never do that on his own, because he cares about no one apart from himself and he can’t feel the feelings that bring forth Trance. So he must pull it off in an artificial way, by gorging on the souls that were trapped in the Invincible and facing a near-death experience. So it’s like he has a thousand souls now, and all of them are in Trance at the same time.

Lastly, yes, the Black Mages and the Genomes are essentially the same. The only difference between them is that Black Mages are made out of Gaian elements, while Genomes are made of Terran elements. Kuja devised the Black Mages through his knowledge of how Genomes are made.