How to draw an icon with rough background like that:
Is it possible to do this with some fill tool?
An easy way to make line textures and cloth textures in Paint.NET is to draw many parallel lines and use Fragment. Draw vertical lines and fragment, then overlay horizontal lines on a separate layer and fragment those. Merge the two layers and shrink the texture.
I kept the pattern separate from the white background, then colored the lines and lowered alpha with Channel Ops plugin to get a close approximation to what you have above.