
I’m confused how is him being a teacher helping him?

This^^^^^^^
Plus since he was "suspicious" he didn't really had any say in that matter. It was a mean to watch his every move (HE EVEN HAD A TRACER LIKE A CRIMINAL LMAOO). Also being close to his father/the director will help finding his younger self as stated in his "teacher" contract lol
(Source: How I understood it-)

I’m so confused why does he want to save her so bad? It seems like a big hassle for nothing

This isn't much of a spoiler.
They were very close in the past life and i think one of them liked the other. Also, the princess had given up her own life in regret to protect the people. So it's pretty much that she's not a bad person and might be useful and also he considers her as a friend due to his past experience.

Honestly what is going on? I dont get it anymore

I’m all caught up and when they had there break I was waiting for the new chapters. Yeah the few chapters feel like fillers I am waiting for something to happen. I’m just confused on the plot. The mc is a hostage, the girl is going to disappear and the original girl is going to come back? And the guy has a cursed of being a child. There is no clue goal

I think because that's his goal. To not follow the book, i e., not interacting with the MCs. He doesn't have a goal to change the novel setting or even the thought of finding a way back. However as we read on, he starts having encounters with other characters of the novel and in turn giving him responsibilities. Its a slow burn type of read.
I’m shocked she didn’t get in trouble for letting him in
well,, they cant really stop the dude in this situation when she saw him passed out
She literally open the door and shown the duke the keys. They didn’t know he was passed out
cant really defend that lmao and when the dude tried to threat the duke, i just really wanted to gauge his eyes out haha