One common theme is friendship. Since Saiki has a group of friends in the original show, fanfictions often explore their relationships deeper. Another theme is power management. Saiki has to constantly hide his powers, and fanfictions might show different ways he has to deal with that in new situations.
Sure. There are many great fanfictions out there. You can start by looking on popular fanfiction websites like Archive of Our Own. Some fanfictions might focus on different relationships in the show, like Saiki's interactions with his friends in new and interesting scenarios.
The Saiki K manga ended. It wrapped up the storylines and gave a satisfying conclusion to the readers. Although it's over, it still holds a special place in the hearts of fans.