Desktop Toolbar

This is impossible to make the toolbar that 100% looks like the desktop toolbar. Actually selecting the desktop folder (/Users/martin/Desktop) as TLB toolbar folder is not recommended because TLB creates there some internal files in the toolbar folder (on the desktop in your case).

If I create a menu and select the predefined Desktop menu option, it contains all the icons. So my question comes down to how I can create a standalone toolbar with all the icons that appear on a Desktop menu

The menu is the only way to show all desktop icons. In addition you can setup toolbar to show the menus without click (on mouse hover). And the free space on the toolbar you can use for something other. TLB gives much more ways to organize your workspace.