the models won't export.

Yeah, I'll try it now. So, they use TGA for regular textures and DDS for 3D coatings?

Added 41 minutes later
Okay, it worked. The only thing is: for some reason, the horse has become a bit whiter, and a white background has appeared around the chains, which I definitely didn't create.

TGA is used as a source file: it's not used directly. You can export it to DDS using an editor.

Regarding the background. I'm not entirely sure, but a completely transparent background should be black. This could also happen if the alphaMode parameter of the material is filled in incorrectly. Different combinations of transparent/opaque texture areas require a specific alphaMode. AM_ALPHA_TEST (1-bit alpha) would be suitable for the knight.