I'm having trouble understanding the part about right clicking your desktop to copy/paste a shortcut....??? I've used the deskCut extension for so long in my FF that I've forgotten how shortcuts were made before.
But you might try this to fix the icons reverting to IE. Open IE properties and reset IE as your default browser in the Programs tab. Save a shortcut in IE from any site. Now, open FF and if a window doesn't come up asking if you want to make it your default browser, then go into Tools-Options and do it from there. Put a check in Always check at startup to see if FF is the default browser and click "Check Now". I think then an option will come up to set FF as your default. If this fixes the icons (the one you saved from IE should change to the FF icon), then you can go back in FF and uncheck the "always check at startup etc" so you won't be bothered with that anymore.
If that doesn't work then it's probably got something to do with your file associations in Windows Explorer (not Internet Explorer) up in Tools-Folder Options-View Files or your shell extensions.
OR...do you have other users on your computer and they prefer IE? That could be conflicting. Take a look at this.
DefaultBrowser allows you to set a default browser on a per-user basis. Unlike the standard XP configuration, this tool allows each user to set their own default web browser without affecting the other user profiles. It comes with a few popular browsers to choose from and you can configure any other browser by specifying the path to the executable file.http://www.snapfiles.com/get/defaultbrowser.htmlhttp://www.snapfiles.com/opinions/DefaultB...ultBrowser.html
(Each user can set their own preference when they are logged into XP.)
Actually, you might try that little program even if it's just you on the computer and maybe you won't have to go through all the other steps I mentioned.