It focuses on the story of L's early days and how he solves cases. In this novel, we see L's unique detective methods and his battle of wits against various criminals.
Light dies when his name is written in the Death Note by Ryuk. Ryuk, who was the shinigami that gave Light the Death Note, decided to end it as per the rules.
In fact, the manga of Death Note has its unique ending that sets it apart. It's a conclusion crafted specifically for the original comic format, with elements and developments not found in other versions.
No. Once Light dies in the Death Note manga, that marks the end of the core story. There may be spin-offs or related works, but the main narrative doesn't carry on from that point.