What are the requirments for a faction icon because i made an icon but when i run CC it ends up looking like this

Put it into the palette properly.

If you use the search toolbar you're sure to find a tutorial.

As for size, there are no limits to that. Usually try to keep it under 40x40 pixels, but even if you dont CC will simply resize your icon.

It is just over 40x40 at 51x44 but CC should just resize it right? I know it should be a .bmp but does it matter whether it is a 16 or 256 color or 24-bit bitmap? Also, i used the purple shade that CC negates to give it a clear background. Does thats work or does it need to have a solid color background? Finaly,
What Palette is there?

Yes, it very much does. If your sprite is not in palette, it will look like the mess you currently have there. Cortex sprites (excepting glows) are all 256 color paletted images, using the palette found in base.rte. But! It's not enough to just use the same colors, you must have the image encoded with the same palette.
The easiest way is to make a copy of palette.bmp and paste your sprite into it, using the copy, renamed, as your new sprite.