I apologize on the late response. missed the email notification of your reply.
If it is not working with the featured image, then chances are that the featured image is not what controls that icon on the homepage. Sift through the appearance tab and see if there is a theme options panel. If there is, I am betting there is a place to control which post belongs to which icon.
Although as for placement of the icons, the best I can tell is that it is hardcoded in that order (although I would not know for sure without seeing the theme)
Your 100% best bet would be to contact the developer of the theme if it is not easily done from the theme options panel.
Also (on a side and probably unrelated note) I would mention to the theme developer that they seem to have placed the wp_head() function in the wrong place in the source code. I went to view the source code to look into your problem and I was slightly confused to see so many scripts before the <html> tag even opened. It is supposed to be right before the </head> closing tag.
I apologize that I cannot be of more help, but again your best bet may be to get in touch with the theme developer