7/16/13: All that cardboard along the base of the walls is there for a purpose: they are called voids, and are there to allow for soil expansion. Where the concrete remains is where the caissons are supporting the foundation. The rest is allowed to serve as that buffer for the soil.
7/16/13: Backfilling should take place in a week or two.
7/16/13: One of two drains on the floor of the interior. The drain system has a filtering cloth above a layer of rock and buried pipe that borders the foundation. The cloth and rock filter out dirt and the pipe has holes in the top about every 4 inches. Excess water is collected from around the foundation and, thanks to Mr Gravity, delivered to this and the other drain where a pump (to be installed later) will push it out a 2 inch PVC pipe to the outdoors and away from the house.