what is the right drainage system around a floating crawlspace foundation?
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.