Hi,

Could you screenshot this please?

The Facebook icon (if redirecting to HTML via Firefox) should have the logo of Firefox cause you saved the URL (HTML file) on your browser via Firefox so it set's Firefox's default logo.

Skype is a program, not apart of Firefox so that doesn't have anything to do with this...

Are that links to internet shortcuts that you saved to the desktop?

Such links get the icon of the default browser and you need to change that icon yourself if you want a different icon.
Be aware that Windows resets the icon if you change the default browser.

It would use to populate a company icon if i dragged from address bar or create shortcut. Now it just defaults to fire fox's logo. For example. If I dragged Yahoo icon from address bar. It would put up the yahoo "Y" Now it's generic. I looked to change icon with no luck

Did you previously use IE to create a desktop shortcut?

That doesn't work with Firefox unfortunately.

If you create an internet shortcut by dragging the website favicon on the desktop then that shortcut gets the icon of the default browser.
If you want a different icon (favicon) then you have to assign that icon yourself to the desktop shortcut (right-click: Properties).
You can usually get the favicon if you append "favicon.ico" to the main domain of a website (e.g. http://www.mozilla.com/favicon.ico) to display the favicon in a tab and save that image to a folder or see if you can find it in "Tools > Page Info > Media".