I updated section 4 with a NiAlphaProperty settings subsection. I focused mainly on simple illustrations of what settings do instead of defining what the settings mean. I also added a link to a msdn page about color blending. Alpha blending is a form of color blending using an images alpha channel. Here is the link if you'd like to learn more about how color blending works. Basically, the blending works as follows.
(Source * SourceBlendFactor) + (Destination * DestinationBlendFactor)
"Source" is the color of the model materials in that pixel before blending
"Destination" is the color of what is behind the model in that same pixel before blending
The two values are modified by the value of the blend factor in that same pixel, then they are added together.
Blend Factors/Modes
One - multiply by one (no modification)
Zero - multiply by zero
Src Color - multiply by "Source"
Inv Src Color - multiply by inverse "Source"
Dst Color - multiply by "Destination"
Inv Dst Color - multiply by inverse "Destination"
Src Alpha - multiply by value of the model's alpha channel (diffuse and vertex colors) present at that pixel
Inv Src Alpha - multiply by inverse value of the model's alpha channel (diffuse and vertex colors) present at that pixel
Dst Alpha - multiply by value of the background model's alpha channel (diffuse and vertex colors) present at that pixel
Inv Dst Alpha - multiply by inverse value of the background model's alpha channel (diffuse and vertex colors) present at that pixel
Ok, maybe not so basic. I'll add that to the OP, too.
Now to tackle refraction. I'll take a look at both skysan's and your mod assets and see what I can figure out. From what I know, I can tell you that the refraction works based on surface normals. In the case of a sharp, faceted edge, there is a very immediate hard change in surface normals. I'd guess that the refraction shader wasn't made to handle that situation. This seems more likely given that faceted edges are usually a no-no in games: they cause obvious ugly aliasing effects.