Depending on what hazmat disposal they have, they'd be better off using something like SYBR Safe, especially with beginners. It's almost as good as EtBr for staining, but not toxic. (Downside: it's much more expensive, EtBr is cheap as hell)
That what lab assistant usually says. At uni we used some blue florescent dye that apparently got ionically bonded to P group of DNA backbone. It was completely safe(not carcinogenic). I can't remember the name of the dye, but results with EtBr were much clearer.
If my memory doesn't lie to me, I think its a load dye, which only dyes the DNA sample to visually assist during the loading of the samples into the "wells" of the gel. Otherwise you can't be sure whether you put it inside the well or somewhere into the surrounding buffer.