I have some ideas here ...
for the mattress, you could layer .. we are doing fitted sheet, topsheet, then painting dropcloth over that, then fitted sheet over that, and everything pinned with safety pins. The top sheet is brown and cheap ... doesn't matter any way after wards just soak in plenty of hydrogen peroxide.
For peripads, I made an herbal infusion. The herb mix came with our birthkit, but I'm sure you could find one or make your own... it has uva ursi, yarrow flower, plaintain leaf, sage, witch hazel and comfrey leaf and root. Boil water, turn off flame, through in herbs, steep as long as you want to (for an afternoon). Strain it and pour liquid over peripads to saturate, wrap them in cellophane and place them into a bowl in the freezer (so they become mama shaped).
For the cord, I think we are tying it off, cutting then burning. That is something I saw done in rural Guatemala and thought it was beautiful ... babies rarely got cord infections even though they were living sometimes in places without running water.
For our birth certificate in San Diego, it is really a hassle ... even though we have midwives, we still also have to get letters from three people who can vouch that we had the baby, that she is ours and we are U.S. citizens. It's different in different counties, part of it is that we're so close to the border.