The questions are, as always, silly...
1) How do I remove the white background from creature icons (can you explain it more clearly, as the explanations are too complicated, and I'm almost a novice in this area (if that matters, I use Paint.net))?
2) How do I create icons from scratch?
1) Create a new image (larger than 128x128), delete everything, and reduce it to 128x128. Then, copy the image from the "corrupted" icon without the transparent background and paste it into the file you created earlier.
2) Briefly for Paint: take an image/art/screenshot, make it 256x256, delete everything unnecessary, and outline it with a 4-pixel line. Reduce it to 128x128, and that's it; the background won't be white.