bonusbrain decide the folder icons in the home directory
That is precisely what I mean, you can change whatever you want in your users' home directory. If you are trying to change the used icon from the .desktop file (which it sounds like what you are referring too, still no idea how you enter property from the panel), those files are owned by root, and no distro will let the user alter those, only root can.
So, it seems there is some info missing, do you normally set up a panel in some custom fashion in your home directory? In the properties images from post 3, see the permissions tab, it should say
root for owner. I would like to see an image where a distro alters that ownership (and the .desktop file is in /user/share/applications or something similar)