Nope.

No it does not. They had the concept of it but never went through with it.

Nope, no death trap. Just a weapon and a second tier. You can tell/check what each map has in the map select screen. Green axe shows stage weapons, yellow arrow means mutli tiers, and the skull means there is a death trap(s).
I think originally the glass was supposed to be a death trap though, I remember reading something about the bugs crawling all over the victim and eating them.