is it possible to read the position of a given "icon" on the desktop? Or better, store them all and be able to restore them later (for instance after a change of resolution)?
There are some freeware utilities which you could use, for example
Save and restore the positions of icons. DesktopOK is a small but effective solution for user that have to change the screen resolution often.
To answer the questions in your question detail text, rather than your question title, yes, it's clearly possible :)