Ok, for box squatting: while in the hole, the shins should be vertical, or past vertical toward your heels, according the article. It's somewhat of an exaggeration, but it's meant for getting a huge stretch in the p-chain.
The knees are harder to explain, but I'll try. Stand up on your feet and pretend that your feet are bolted to the floor. Now, try to tear a hole in the floor by forcing your knees out to the sides (toward the outside edge of your shoes). It is similar to trying to rip the bar apart, or "spread the bar apart" when benching. It is hard to explain, but if viewed from the the front, the squat should happen without your legs collapsing in at all (ie-no "knock-kneed" stance). The "spreading the floor" phase has to do with activating your hips/glutes/p-chain by consciously putting the pressure on the outside edges of your shoes.
You should not necessarily physically POINT your knees outward by pointing your toes outward, unless you have flexibility problems.
As far as deadlift stance goes, I think that whatever is comfortable for you to do is optimal at first. Your hand position varies depending on how wide your stance is. Aim for a comfortable position first, and then if you feel the need start tweaking it. For me though, the DL position is easier to feel than to teach. You had a respectable pull before you stopped pounding the heavy weight, so you should be able to feel the right set-up. Don't sweat it. This particular problem will most likely resolve itself as you pay attention to the other basics (shoulders behind bar, etc).