So far I've made about 20 attempts at boxes, but some of them are so distorted I haven't been counting them, only considering 10 of them to be actual boxes. I've been limiting my count to outcomes that have three clear sets of parallel lines. Should I limit myself with this criteria, a different criteria, or not limit myself at all and count every attempt no matter how warped?

I would say count every attempt. This is supposed to be practice not an art piece. If some of your boxes are so distorted you feel bad counting them then maybe you need the feedback from submitting them even more than if your boxes were perfect. Don't assign yourself extra boxes and delay that. You could also post some examples early and see if anyone can see where you're going wrong.

Secondly, I've discovered that rotating the paper helps me to see viable boxes even in what initially may have looked like a bad outcome. The issue is that these boxes work in a vacuum from a certain angle, but not when considered part of a set with surrounding boxes viewed from the same perspective. Should every box on the page work from one perspective, or is it okay to consider them all individual and rotate them freely?

Each box should be considered seperately. It would actually be a mistake to draw them all existing on the same plane.

Just a quick clarification - when you say "that have three clear sets of parallel lines", do you mean lines that are visibly parallel on the page, or edges that are parallel in 3D space? The former would be incorrect - as discussed in the challenge video and notes, your lines are of course meant to converge when drawn on a 2D page. If you mean the latter, then that's fine, nothing to worry about.