Not sure about 24-bit, but that should certainly work. I think for Morrowind, you want to avoid RLE (compressed) TGAs in general.
As for 1024x1024 vs 1024x512, both will work. Only very old cards require square textures, most just want powers of 2 (and new ones don't even care about that, though Morrowind still does). TGA and BMP work from 2x2 to 2048x2048, DDS from 4x4 to 2048x2048 (you might be able to do 4096 or 8192, but I don't know if those work in Morrowind).
Edit: Also, while 2x2048 may work, it also makes a
mess of video memory. A 512x512 texture usually takes a square in memory. 512x1024 is a rectangle. Imagine textures are squares of construction paper and you have to pin them onto a cork board, and avoid moving previously pinned ones. It's pretty obvious how long and thin textures mess with the space others can use.