Also check out 'The Last Days of Krypton' by Kevin Anderson - it's out in paperback.
Traditionally, the only survivors of Krypton were the inhabitants of Argo City (who died later), the inhabitants of Kandor (the city was stolen by Brainiac) and the Phantom Zone prisoners.
L&C added the colony of New Krypton.
Prior to Superman the Movie, Krypton was an idyllic, probably technocratic, society. Jor-El was a brilliant up-and-coming scientist with a fixation on the world ending.
In Superman the Movie, Jor-El was a scientific and political leader (with a fixation on the world ending.) However, instead of an idyllic, garden planet, it became an ice world ruled by an autocratic council of elders.
The Superman universe re-set (which L&C is based on) had Krypton being much like Earth in that it had a rich and occasionally violent history. Jor-El was a senior scientist whose research and conclusions were considered too far outside the accepted norms.
You can assume that Zara's description of New Krypton is a simplified reflection of Old Krypton.
In the Movies, Krypton was taken out when its star exploded.
In L&C, it's pretty obvious it was the planet. (We're not going to discuss the impossibility of the ship's nav device seeing the ship escape the planet.)
One traditional explanation was that an experiment (or a doomsday device of some nature) converted the planet's core (traditionally uranium) into kryptonite. This lead to instabilities in the planet's structure leading it to violently disintegrate.
