No, your background does not work, because the path you entered is relative to the css file.
Code:
body {
background: url(skins/parabola/img/background.jpg) top center;
}
So the css file is in skins/parabola/
Your code looks for skins/parabola/skins/parabola/img/background.jpg , which i highly doubt you have in your skins folder
img/background.jpg would be the correct path
Taking it a step further, i would upload nothing to the core parabola, also not img.
If you have new images i would do child/img/myimage.png to prevent a possible overwrite on skin updates