Let's fix the duplicate icon first, open Firefox from the pinned icon you have already after the second one opens up unpin the first one and pin the second one that should stop the duplicate icon.
Now the icon go to C:\Users\YOUR USER NAME\AppData
\Roaming\Microsoft\Internet Explorer\Quick Launch\User Pinned\TaskBar then right-click on the Firefox shortcut click on properties make sure you're in the Shortcut tab and click on the Change Icon Button. After you open up Firefox again icon will revert back to the default icon because it opens up Firefox.exe you would have to change the icon in the .exe for a permanent change. AppData
is hidden is this tutorial Step #3 to unhide it File and Folder - Hide or Unhide