Tbh I haven't fleshed out the world itself a lot, BUT the characters are pretty well documented!
the basic premise is that Penelope Gecko falls asleep in class during the day, and fights monsters by night. The main trio all have "focuses" that act as manifestations of their magic!
Their magic directly correlates to something about their personalities: Penny has the offensive type, as she's aggressive and bold. Elias has the defensive type, as he has trouble opening up to others. Kio has the trap type, as he puts up a facade to keep people happy.
Now, below is the deeper, slightly disjointed stuff:
Penny was adopted by Demitri after her real father died mysteriously, leaving her as a baby with no immediate family to live with. Demitri was the only contact in the guy's phone, so the authorities dropped Penny off and said "we'll pick her up when we close the case." Then the case took like 6 months to close so by the time they came back Demitri was like "actually can I just keep her" so the authorities shrugged and said sure. Hence, their different last names. Demitri knew Penny's real father only by face and name, nothing deeper. He met the guy at a wedding he was hired to shoot at, so he just assumed the man was a friend of the family, but it came out later he wasn't...
Kio was raised with his older sister, Kotone, by their father Koshiro. He ADOREDD her, would practically follow her every step. Even as they both got older and started antagonizing each other as siblings do, he always idolized her. She really was the world to him. She unfortunately took her own life at the ripe age of 13, and Kio hasn't really been the same since. Now, 12 years old, he's quieter than ever, and Koshiro's starting to get worried. The only person Kio still finds the will to antagonize is his old babysitter, Penny. Kio believes monsters are real long before they actually stumble across any (read: werewolves, vampires, goop), but he has one stern rule: ghosts don't exist!
Elias is a pretty ordinary guy. Or at least, he tries to be. His appearance makes him stand out a lot, so he counters this by retreating into a shell when anyone tries to approach him. He's lucky his dad's band, Steel Your Love, is still so underground, otherwise people might recognize his cool custom merch that he's always wearing. Speaking of Lucky: he has a rambunctious kid sister who insists on the existence of aliens. She couldn't care less about monsters, though, and simply thinks Elias is teasing her whenever he mentions them.
There are some other side characters that hold variable amounts of relevance, but this is all the core stuff 💭