Naruto: I Become the Strongest Ninja Through Sign-In Rewards

I didn't understand it at the end.

Is this some kind of supernatural book? Each chapter introduces a new protagonist. The protagonist was called Mu in the beginning, then the name was changed. And this is only in the first few chapters. Earlier, Kakashi clearly accepted the mission, but in the next chapter, Hayate is leading the team. Hayate Kakashi, right?

Yes, I was initially rewarded with Sage Mode at the start of the game, then learned it again later and used it when fighting Deidara and Sasori. I learned it again around chapter 80.

What does it mean to use the Mangekyou Sharingan as a Chunin?

You already have 3 Heavenly Books