The following information was found in BROKEN FORTUNES: SOUTH CAROLINA DEAD IN CSA SERVICE 1861-1865, by Randolph W. Kirkland, Jr.:

John HATCHER, Co. D, 14th SC Infantry, was from Edgefield District. He enlisted at age 28, and died of pneumonia at Fredericksburg, VA, on 10 Jan 1863.

John G. HATCHER, Co. B, 19th SC Infantry, was from Edgefield District. He enlisted at age 18, and was killed at Chickamauga, GA, 20 Sep 1863. He is buried in the family cemetery at Trenton, SC.

From DARK HOURS: SOUTH CAROLINA SOLDIERS, SAILORS AND CITIZENS HELD IN U.S. PRISONS 1861-1865, by Randolph W. Kirkland, Jr.:

John HATCHER, Co. I, 2d SC Infantry, was captured at Cedar Creek, VA, on 19 Oct 1864. He was imprisoned at Point Lookout, MD, and exchanged on 17 Jan 1865. No age or residence is given.

I'm not aware of any on-line descriptive rolls for the regiments mentioned in your original post. The service records of the various John HATCHERs may help you identify them further, but they typically contain little personal information other than age and place of entlistment.

Hope this helps a little, and good luck.