Book confirming the church is purposely making sure technology doesn't advance going of their way to destroy technology and keep inventors directly under their control to sabotage their efforts. In fact outright specifically states that Rhea had the printing press banned when it was invented due to worries of increased literacy among the population. Also Rhea was the one that started the fire where Jeralt left the monastery with baby Byleth. She was trying to burn a lot of history books so she could rewrite history as she saw fit.
If that's true, then Edelgard was 110% right about Rhea.
Kill her, absolutely. Book burning and suppressing literacy is absolutely abhorrent and alarming.
Any contact with the chamber floor will result in an 'unsatisfactory' mark on your official testing record followed by death. Good luck!