Back in 2010/2011, this image was used in the Ben Drowned ARG. In 2019, a cropped version of this image was used on the cover of the Turkish book Gökteki Ay Üşüyor by İbrahim Kalkan. The only other results I can find when reverse image searching are a Youtube video (with no sourcing), a Powerpoint presentation where the image is used as a background (of course it's not sourced), and those HD wallpaper reposting sites (where again, it's not sourced).
I don't know anyone who knows Turkish and the book only shows up in exclusively Turkish results, so I have no way of investigating whether the book sources the image at all. Though considering the image's source couldn't be found by other people in 2019, it's doubtful the author of that book had the source either.
The wallpaper reposting sites had the image as early as 2007, so it could be from 2007 and earlier.
Probably the background comes from the anime version of that manga.
Unfortunately not. That fanart is from 2008 and the tree image has been found with upload dates elsewhere early as 2007 Though through reverse image search I found this fanart's from earlier than the results I've found, I still can't find a source for the background.. I've also looked up and down and not found any Rozen Maiden art that has that image in it except for this specific fanart.