I wanted to test exporting with 2.79, but I don't have nif scripts installed for it.
Anyway, the reason there are two meshes is you have two materials assigned in 2.79 (although, not in 2.49). This extra material is created when you import "obj" format for some reason. Looks like you already deleted it in 2.49. It's worth noting if you want to separate parts of a mesh on purpose you can create a new material. Then select the faces you want separate, and assign the new material to that( like if you only want team color/gloss for those parts, ect).
Here is the export settings I have for 2.49. The only thing I ever change is switch to animation(kf) only for exporting KFs, and set the scale to 1 (from 10) for civ 5 units. Some people think "Stich strips" is better. I don't know. I don't see a benefit, but I don't know everything.
As for setting up the texture for the material. It sounds more complicated than it is. It literally takes like 15 seconds to do, but seems complicated when you spell it out).
Starting in the object 3D view. Press "Ctrl + Right Arrow" to switch to material view.
At the bottom press the texture tab (square) next to the material tab (sphere).
Select "add new. Then in texture type select image. I think this is image/video in 2.79)
Then select "load", and browse to where the dds file is located (Gimped.bst_minotaur_head_01_diffuse.dds).
At the bottom switch back to material (sphere tab).
Set the map input to "UV" from "Orco".
Done in material view. So, press "Ctrl + Left Arrow" to switch back to 3D view.
Nothing will apparently change, but if you exported right away the nif should now have a texture property. However, to actually see it you have to go to edit mode, and bring up the UV editor in the window below.
The "minotaur_head_01_diffuse.dds" will now be available.
Yeah, it's upside down.
In the UV window select all (Ctrl + A). Then press "M" (not ctrl + M in the screenshot) for "Mirror". "X" is side to side, and "Y" is up and down. There you go. Looks cool.
As for why the original dds files wouldn't load? I donno. They are in DXT10 format instead of the usual DXT3 or 5. Maybe blender doesn't like that? Otherwise they seem ordinary to me.