Okay, nailing stuff that I know:
Site Cap after civ creation
Determines how many civilations are required. Each civ has its own biome requirements.
Dwarves require a "fair"-sized mountain range to flourish. I've noticed that when the elevation mesh emphasizes "low" elevation that there are few (single-digit numbers) dwarven civs. Altering that mesh to emphasize the highest setting on par to the rest will yield a couple dozen (although they won't necessarily survive world-gen.) I'm sure that the same applies to humans, elves, and goblins as those are the other civ-capable species.
Percentage of beasts dead for stoppage
Already been nailed.
Cull Unimportant historical figures
Important figures I'd imagine would be heads of state: generals, monarchs, liaisons, etc. Heroes that have vanquished semi- and megabeasts I'm pretty sure would also count towards it.
Min/Max Elevation
Oceans, wetlands, and deserts can only be created in elevations between 1 and 99. Mountains require 300 to 400.
Rainfall - What are the effects of rainfall besides filling murky pools, unhappy thoughts, and being required by certain biomes?
Grasslands won't generate if rainfall is higher than 33. Rocky Wastelands are probably high-elevation no-rainfall zones.
Drainage - What does drainage do other than being required by certain biomes?
Mesh Size
Easiest way to relate to mesh size is to look at wire mesh. The finer mesh has more inside it. The weight means that any given point on the mesh (where x-axis meets y-axis) has a chance to be that. Locking the mesh size to both extremes (like 5,0,0,0,5) will still have worlds with the mid-values. I've not experimented with extreme values such as 1000.
Minimum mountain peak number - What's the point of this parameter? I mean why does anyone care about peaks?
Having no mountain peaks doesn't affect world gen, although I'm not sure how it affects dwarven civs.
Partial/Complete Edge Oceans - How are partial and edge defined?
A guess here, but it's probably how much of the ocean is on the map. If, say, 5% of the ocean's tiles are off-map, then it's a partial ocean. If half of it is off-map, then it's a complete ocean.
Minimum initial/final X region count - What exactly is a region or subregion and how does it differ from a biome?
A region is an area that has the same designation (temp, rainfall, volcanism, etc.) Sub-regions are probably where each region overlaps other regions.
Erosion Cycle Count - Does anyone know of any guidelines on what values of this result in what effects?
Natural erosion on the world, before rivers and lakes and the like. I'm pretty sure that longer erosion cycle means flatter/smoother worlds. I've watched mountain ranges wither into forests (especially when the value is jacked up beyond the max.)
Max number of subregions - What's a subregion and whats the practical impact of changing this?
More sub-regions means more allowed diversity between areas and their resources.
Temperature is really, really weird. I've set my worlds to generate at exactly 75 for awhile now, but I still get tundra and cold environs.