A few issues. First off, you might want to start with a prologue. This seems like a very specific world where people have grown up with the supernatural aspects as if it were gravity, so some explanation on that is needed. I'd also suggest opening up on a more human scene where we get introduced to the mc a little more before the inciting incident. There's also some moments that are kind of jarring to read, like this paragraph,
The next day, Klein was, comparably, already far ahead than others in his school in terms of completing his tasks. He was determined and was basically doing his tasks at the speed of sound. Klein got bored of doing the tasks and decided to call his friend Steve
It tripped me like crazy when I read he got bored and called his friend right after I read he was doing everything at great speed out of determination(side note, I miss undertale. Does anyone still remember that game). The conversation with his friend is also incredibly jarring, actually, it's way more jarring, like, I got whiplash reading it jarring. You can't have someone open up with I'm good and then bragging about how many tasks they've done when one of their supposed best friend's have died doing said tasks, it just doesn't work. His mother suddenly coming in and boarding up the place also needs more explanation. Since I don't have a grasp on the mc I also don't understand why he's going so far to complete this task to the point of breaking into a museum and stealing.
Honestly, right now this chapter is a mess. I'm not saying there's nothing good here, some interesting ideas are on display and I like the idea of the trials, you've also obviously put quite a bit of thought into it, but it needs some serious work.
My biggest advice is to SLOW DOWN. This first chapter is going at a hundred miles per hour and it makes me not feel any of it. There's enough events here to make three to four chapters, just flesh out scenes. Have him spend more time at the house when he wakes up, talk about his living conditions, social class, age, family matters, the basics, give us some idea of who he is, you can even slip in some worldbuilding. Introduce his two friends when he gets to the school instead of going straight to the trial, have them gossip about what they think is going on, introduce the mcs reason for wanting to win, develop a bit of a rivalry between him and the friend who dies so that it hits harder. Don't have the doctor's react to the mc that way in front of him, have it be behind closed doors and he overhears or something(How he overhears can be a character building moment.) Pick out some of the more fun events and show him doing them, have his family comment on their thoughts on it, you can even seed the mother putting him in lockdown here, maybe even have him do a few task with his friends, really earn that incoming death(Well, as much as you can in three chapters). Have the one friend die as planned, instead of having the two truck along with barely a bump, have the other one drop out, and have the mc seriously question whether it's worth it before continuing. Slow moments like these might seem unnecessary, but they're what really makes a story a story, they give weight and power to the big scenes. Right now it reads closer to an outline.
My smaller advice is for character dialogue. When you have characters talk to each other, before you write any of it, think about what information you want conveyed to the audience, what the relationship between the characters are, and what each character's current mood is before you have them talk. If you're having trouble with it then write out the conversation normally first, reread it, and then break it down into those three categories and make the changes.
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