The story of Superboy-Prime is that he's a version of Superman from a pocket dimension created by the Time Trapper, a Legion of Superheroes villain. The time trapper created our universe down o every last detail until Superman arrived on Earth as a baby, after which it was made to where he would be the only superhero in that world. Although characters like Bruce Wayne, Hal Jordan and Oliver Queen exist, none of them ever became superheroes.
The reason he's so much stronger and not as strongly effected by Kryptonite is because the Time Trapper created him artificially so his cells absorbed and stored sunlight far more efficiently than our Superman.
Also, there were no Green Lanterns or other cosmic entities because the Time Trapper created the pocket dimension with only two planets, Earth and Krypton. Eventually Prime was sealed away in a paradise dimension after Crisis on Infinite Earths. The reason for this was to explain how the Legion could go on adventures with Superboy without Superman ever having been Superboy in the mainstream continuity. The pocket dimension was created so that when the Legion went back in time, instead of coming to our Earth they would go to Earth Prime instead, so there would no longer be a Superboy on the main Earth and the Legion would never visit the past.
There was a story after Crisis where Superman ended up on that Earth and it was explained why he had no recollection of it and why there were no other superheroes. Also, Luthor was good and created a Supergirl called matrix who was a synthetic being made to fill the void, given the memories and appearance of Lana Lang who was engaged to that version of Luthor and had passed away. She became the only survivor after General Zod and his cronies escaped the Phantom Zone and laid waste to the people of Earth Prime, with a mangled and amnesiac matrix barely surviving. Superman, in a fit of rage, killed Zod and his cronies using kryptonite that existed only on Earth-Prime and didn't affect the main continuity version of Superman because of his different genetic makeup, but were able to kill Zod and crew. He carried that guilt with him for a long time and took Matrix back with him and left her in the care of Ma and Pa Kent. She later became the 90’s version of Supergirl eventually.
So that's why there was no Prime version of any other characters aside from Superboy. In that world, they didn't need to because any danger was manufactured to were Superboy could take care of it and they didn't need other heroes.