There are too many questions in this to do a good job of answering so I will tackle the most important one.
I would build a French drain from above the house along the property line: build it as high up the property as you can afford to go and at least 3' deep. The depth will help capture both surface and subsurface water movement. If you also have water coming down the slope to the top of the property, a drain 20-30' in front of the house that is higher on one side sloping down to where it can tie into the property line drain would be the best starting point to try and reduce the water issues.
If there is still standing water in the lowest corner, you may have to dig a trench under the footer and install another drain there, though not as deep as the main one along the property line going straight downhill until it is at the surface and gravity will keep the crawl space dry.
When I put drains in I use the perforated pipe that comes in a sock. It prevents the small gravel from getting in the holes and filling the pipe. pipe in sock it cost more but really helps over the years.
Where I live, we have ground water issues year around. This is obviously subterranean water, (i.e.: you say, not roof, no water leak, etc. I also assume no window leaks, because you say it's in the recessed room...only.)
Your first paragraph is powerful. Because the ground seems to "go down towards the foundation," I suspect there is a subterranean water problem caused by: 1) shallow water table, and/or 2) subterranean water pressure.
1) Shallow water table: if the "area" around your home is generally flat, rain will greatly affect the water table. You say, "have not had a heavy rain in over a week, maybe two," makes me think you get "heavy rain" from time to time. If so, that water will make the water table rise and put water "pressure" on the bottom of your slab...especially the lowest slab.
Where I live, we'll install French drains under slabs to make sure the water from the water table is diverted away. Btw, those roof drains that you connected, did you extend them to a stormwater system, or just run them to a ditch where they can seep back down in the ground?
2) Subterranean water pressure: if you live near a hill, the water table will generally follow the slope of the hill. If your homesite was cleared off along that slope, (or especially if you live near the base of a hill,) the pressure from the water table above your home will push on the water table at the base of the hill and cause the water table to rise. This is called Subterranean Water Pressure AND it will put water pressure on the bottom of your slab.
The only way to relieve this pressure is to install French drains around your house. The size and depth depends on your site, (slope,etc.) and soil conditions. Remember, you are trying to lower the water table. So, after you gather the water in the French drain, make sure it is discharged off site. Don't let it seep back in the ground. This may take a pump.
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Some wood species hold up well outdoors even without a surface treatment (like cedar and redwood). I can't tell by the photos what type of wood your deck is made of. That being said, it certainly would not hurt to treat it. It would help stabilise the the color and protect the wood.
The type of coating is up to you, but my preference wood be a high quality semi-transparent stain. The amount you need depends on size and various other factors, follow the directions on the can.