If the bunk bed does not have a rail, you can ask for one (at no cost). I wouldn’t be terribly worried about falling off, though; do you fall off your bed when it’s on the ground? Barton (which has a lot of lofted beds) has some beds with a railing and some without. Some students use a ladder and some students climb the end of the bed which has rungs.
I don’t know with certainty how much weight a bunked bed can hold, but I will say this: students sometimes hang out with 3-4 students sitting on the top bed. Some students also have significant others sleep overnight in the same bed. This is an engineering school – we aren’t going to put you in a bunk bed that can’t stably hold a student, a laptop, and a backpack…