When I now use the icon in an plan the lines are not always visible in all zoom levels, how can I fix this?

I've seen something similar and it is always with SVG and thin lines. Just a guess, but it might have something to do with the calculation of the SVG data towards the screen display. Sometimes very thin lines seem to "fall between pixels" (of course not, but it looks like that).
Try converting the image to a PNG and use it as a plan icon. For me it solved it in most cases. If that still doesn't work try thickening the very thin lines.

What is the best way to create good images for the floorplan and floorplanicon? I could not find good information on this.

Any image creation program you feel comfortable with will do. For example GIMP or Krita. Sweet Home 3D can handle different image formats but I mostly use PNG, it scales well and supports transparency.