NZ White rabbit kit death

by Brittany-Mari Sullivan
(Greensboro, NC)

So I wrote here several weeks ago about how my NZ White mother wouldn't care for her 4 kits that later died while I was trying to take care of them... well about a month ago she had another litter of 8 and after separating the male the mother made a nestbox of her own and was taking care of them. Today after checking up on them, I noticed one of the skinnier ones had died. They are at least a month old and seemingly healthy and I'm trying to figure out what went wrong. Here are some questions I have for anyone that could help me:
I often notice a few rabbits always trying to get at the mother's nipple and sometimes she almost steps on them to get away to jump on top of her shelf to get away from that... could she not be feeding them enough?
My husband set up the cage and Im not entirely sure how clean it needs to be to make sure its free of disease... its mesh wire and wood along the sides and thr mesh wire is on the bottom as well. Most of their poop goes right through and onto the ground about two feet below it... This is probably highly unsanity isnt it? Could this cause them to get sick? Does the poop need to be shoveled away from the ground beneath them even if the cage is raised?
How do you properly clean this kinds of cages?
Should I be taking out the kits to feed them separately to make so their eating enough?
Ive learned not to bathe kits but the bpttoms of their paws are always yellowish - is that a sign of sickness or anything?

Thank you