You are not likely to find much more information on the 4th Regiment, French Brigade, because there are practically no records of the Louisiana militia. As for the 22nd Louisiana Consolidated Infantry, you will find a short historical summary in my book "Guide to Louisiana Confederate Military Units, 1861-1865" (LSU Press, 1989). A more detailed history appears in my article "The Twenty-Second Louisiana Consolidated Infantry in the Defense of Mobile, 1864-1865," which appeared in "Alabama Historical Quarterly," Vol. XXXVIII (1976), pp. 204-213.
S.O. #113 refers to Special Order No. 113, which was probably issued by the District of Mobile. Special orders frequently assigned soldiers from their regiments to detailed or special duties. It is possible that the full text of the order is in the records of the District of Mobile in the National Archives in Washington, D. C.