a) The code I suggested would make the bg of the gallery carousel display your blugreen textured image. If it didn't do it, that's because you've already added a similar code to add a white bg, and the one code overrides the other.
b) But my reply was wrong anyway: I was confused because of mattwiebe's reply and your question about the "Your Background Here" comment. I paid more attention to that instead of your original question.
c) You've set the images to link to the image file when clicked. The bg you see in that case is not part of your blog, it's just a new browser window or tab with the image on it. If you want clickable images with a bg you can control, set them to link to attachment pages.
d) Your images are impossibly large. The one I checked is 4368x2912px, size 3MB. There's no point uploading such huge files: nobody has a 4368 wide screen, so you're just slowing down the loading time of your pages and wasting your storage space. If you decide to make the images link to attachment pages, you should use an image editing application to downsize copies of the images to maximum 960px wide, and upload and insert these copies.