Maybe the combined minds here can help you find more natural solutions to your issues
The first thing I would say is that, french drains or no, you need to do a lot of digging to get the ground surface behind the house sloping away for at least a few feet, and positively draining around to the downhill side. No matter what materials you use in the house, you will probably have damp until you address that. It may sound like an impossible job, but if you are in decent shape and the ground is not very rocky, you
should be able to dig a few feet a day, and before long it will be done.
When you replace the failing retaining wall, don't succumb to "neatness" and build it vertical; build it with a slope back into the hill of something like 1 in 6 (4" for a 2' wall). This will make it much more stable without the expense of deep footings and rebar.
You will likely need to use some sort of waterproof material at the base of your walls, be it plastic or masonry. Even rot-resistant
wood will wick moisture up into the rest of the wall.
Alternatives that occur to me are making the bottom 6-8" concrete or masonry, finished smooth on the inside, with your wooden walls on top, and accept that there is a strip at the base that is a different material.
If you can dig the ground outside to 6" below floor level sloping away, then you can build masonry foundation up to floor level and conventional walls from the floor up.
If you can deal with a step up into the back room(s), you could raise the floor level in those rooms so that you can have foundation up to floor level with standard walls, and not have to dig so deep outside.
It looks like you will have to completely tear up and replace the floor structure, so that gives you the chance to do more digging (!) and get a crawl space where you can put vapor barrier down on the dirt. As I found as a teenager helping my father upgrade under the bedroom wing of the house he had built, that vapor barrier makes a huge difference by itself.
Another possibility would be to put in gravel, vapor barrier and a concrete slab.
I look forward to other ideas on this case.