Do DDS files support alpha transparency AKA partial transparency?

Put simply: Yes.

DDS files may include an alpha layer. Here's a tut on how to add alpha transparency to a DDS: http://www.mwmythicmods.com/Archives/CS/Alpha%20Transparency%20Tutorial%20&%20DDS%20Utilities%20Help.htm

Yes - but you need to be sure that when saving you use a compression format that saves the alpha channel !! (DXT3 or DXT5 for example and not DXT1) -- also transparency is controlled by the alpha channel of the .dds file not the normal map (_n.dds) alpha channel which controls the light reflectivity

Also note that it won't do anything if the .nif it's applied to doesn't have the alpha property added to it in the right place.