I think I have an answer to your second question. Remember what he was going on his little tangent about who he was killing? He mainly listed off people who annoyed him. And through the chapters he outright insulted his classmates or in his mind was just ignoring them and was giving auto-replies. Prince didn't want to kill random people he was aiming for all the people who annoyed him the most except his mom and dad, Yamazaki, and Yoichi. And it seemed like those people were his classmates.
My theory is that the prince's brother was bad actor, so when it was his turn to be "interrogated", he showed out expression/emotions that help policeman saw through. After that, the brother had collaborate with the MC, that was why he wasn't surprised seeing MC and policeman stepped out of the curtain
The only thing is not clear to me is, when the protagonist find out that there is a conductor and they went to look for people those 7 suspects contacted that day ... how they made sure other people were not the conductor but prince's brother ? Author should have explain that part .
Also why prince keep on killing his classmates when it's would've been much more wise decision to kill random people and since he has a perfect demeanor it's not like it would be much hard for him collect phone numbers ?