Maybe it's because in all get flailing about Uraraka somehow got herself and activated her powers. (Least that's what I assumed happened)
She was hiding her own face. That means her "finger pads" (which, as we know, activate her powers) were in contact with her own body.
Didn't Todoroki and Yaoyorozu skip the entrance exam and get in on recommendation? The one who scored the highest on the exam was Bakugou.
Mistranslation: Inasa is supposed to be the top RECCOMENDED student. I'm guessing that means he got a reccomendation for Yuuei, but declined it in favor of Shiketsu.