Omega tends to mess around with the texture contents (So it'll never be able to do paletized textures unless someone fixes that), but your problem is that you didn't saved the texture as an 8-bit palleted bmp before sending it to Omega. That's what causes the fully black/trasparent texture.
Anyway, here's a way to make a correct duplicate.
- Export the BMP texture as an 8-bit (256 colors) palletized texture. Make sure you use the original palette (Rip it from an original BMP, exported from TEX via Omega).
- Save the texture as a new TEX via Image2TEX.exe, not Omega.
- Use an hexadecimal editor (HxD is freeware, for example) to copy the first 1260 bytes from the original TEX file and overwrite the first 1260 bytes from your edited TEX. Make sure you don't just paste it and make the file larger.
- Test the texture and the palettes with Omega.
That should do the trick. I personally like to paste stuff with TileMolester, but that's another valid approach, if you know what are you doing with palettes.