Hey Roy --
Sorry I missed this post.
1. I want the main content, header and sidebar background to be another color (all the same, but other than white I mean). Of course I can edit the stylesheet, but I would rather use the 'custom CSS' option. My CSS is not that good though...;
What's your question? Are you asking how to make those areas a different color in CSS?
2. Same for removing all shadow effects on texts and text colors;
To remove the text-shadow, simply do:
3. I noticed that on a wide screen, the custom background shows, but on a 'normal' monitor, the content stretches to both ends of the screen. Can I edit things so that the background is always present?;
Not sure what you mean by "normal" and "wide screen" monitors. The content area is set to 1180 px wide, which is fairly standard for modern displays. If you aren't seeing the background, it's probably because your display is smaller than 1180 px wide -- which is to say that you are in the bottom 10% of display resolutions as of January 2013.
4. The add favicon option does not work (the way I expect). I can add as many images as I want, but the screen looks adding an image to a post (including the 'add to post' option), but nothing happens and I have no idea how to make a favicon of it. Of course I can also do that manually, but since the option is there, some more info might be helpfull.
The "Insert into post" button exists because I'm using the built-in WordPress media uploader function. Clicking "insert into post" will copy the URL to the image file into the input box for the favicon. The favicon will not display until the options are saved and only after you've clicked "insert into post". You can also just enter a URL to an image file manually.
Keep in mind that not all image files are supported as favicons by all browsers. .ico files are supported universally, and .png files are supported by many, but .jpg files, .gif files and others may not be supported by every browser.