The search feature on this forum is not he most user-friendly I've ever seen. I understand that frustration. Never be afraid to start a new thread on here, even if it is a common topic. It keeps the forum going and often those questions are easier to answer.
how deep should the bedding be and how tall can the lip on the nesting box be in order to keep that bedding in?
In some ways that depends on what bedding you are using. We use all kinds of different things; wood shavings, straw, hay, carpet, old feed bags, Spanish moss, rags, shredded paper, and who knows what else. And our nests look different, just all kinds of designs out there. Of course you are going to get different results.
Chickens often scratch and rearrange the bedding as they prepare to lay an egg. This can leave the bottom of a nest bare.
I cut and dry tall grasses, including stems and seed heads, from places I don't mow or weed eat. It's finer and lighter than hay or straw but denser than wood shavings. It's free for a little work. My lip on the nests are probably 4" to 5" high. It keeps the bedding in and I can pile it pretty high if I need to. I regularly hatch chicks in those nests, the babies have no trouble leaving the nest when Mama tells them to.