Yes, that's what they are. If you fall in without the ability to fly, [Lucifer's wings flex at that,] or float, or some sort of magic that will carry you out, you're as good as dead. Do be careful.

[He thinks he's being helpful. Maybe he is, even if it's a bit terrifyingly-stated. His hand is still offered, however, and he patiently waits for her to either stand on her own or accept his help.]

The latter, I cannot answer. I don't know why this happened in the first place, as I wasn't physically within the school when everything... transformed.