Co. "C" was the "Sewanee Rifles" from Davidson County. Here's a regimental history --
http://www.tngennet.org/civilwar/csainf/csa20.html
Pictures such as you request are not as common as might be imagined. It could be a lifetime search with nothing to show for it. Check at the Tennessee State Archives for any that may exist.
Here's a comprehensive website on Camp Chase --
http://www.geocities.com/pentagon/quarters/5109/
Details of Hunt's sojourn at Camp Chase and other records of his service career can be ordered here --