Hi Brendon
In the first photo, I can't tell wehat it's made of from a photo, so I don't know. It looks pretty organic (good). it seems to have some big stuff, but I can;t tell if that's one great big chunk, or a clod composed of finer stuff., Just can't say.
As to the second Q, my GUESS is that any wood chips that have laid on the ground for 15 years have had time to do some composting, so they would PROBABLY not cause much nitrogen deficit even if you tuned them under the soil. I tend not to turn wood under because I had a nasty experience with bags of a cheap, junky soil amendment that was mostly wood chips. that bed was useless for a year as the wood created a big ugl7y mess of fungus underground and nothing wanted to grow there. Your mileage may vary!
If you need to add chunks that big to you soil, for example to increase speed of drainage, it might be OK. To be very safe, you could pile them up into a compost heap for a few months or a year, and "greens" or any nitrogen source, and be sure they were better composted and had plenty of time for fungi to have their way before you add them to your soil.
Ummm ... why turn them into the soil if they are still big chunks? Why not leave them as mulch?
If they have insect or plant disease infestation, you probably should not use them in the soil. Even composting thoroughly might not cure that. In which case, use them as mulch somewhere they won't huurt anything that matters, like foundation plantings of random bushes, or "under some trees".
Is the last photo a "soil settling rate" test? Cool! I've read about them for ages but never done one.
TOTALLY guessing, that looks like a moderate amount of grit, sand and silt. It might have to sit for days for the clay to settle and reveal what % clay you have. But mainly I applaud you for doing it ... I don't know how to interpret it.
Is there a soil scientist in the house??