Run desktop icon as root

As you noted, desktop icons are disabled by default, but you can enable that module if that's something you want, and then put desktop files in the Desktop folder and they will appear on your desktop

What is thinkorswim and why does it need to be run as root? I feel like you're likely doing something "wrong" if you think that's needed anyway. But that being said, if a GUI app needs root (stuff like synaptic, gparted, etc) the easiest way I've found is with pkexec, which uses policykit. It should give you a GUI prompt for your password, and functions similar to sudo but meant for GUI applications. Just prepend it before the app name on the Exec= line of your desktop file, i.e. "Exec=pkexec /opt/thinkorswim/thinkorswim". It has nothing to do with icons tho.