I am researching the family Brig. Gen. George Henry Nixon, who commanded the 13th Mississippi Militia during the War of 1812 and, although I may not be able to specifically address your questions, I hope I perhaps may point you in the right direction.
At the time of the war, Nixon lived in Marion County, Mississippi (Columbia is the county seat) and afterward settled in Hancock County and helped to found the town of Pearlington.I would assume that the unit was raised from that particular area of the state.
At that time, Mississippi was still a territory and you may have luck in locating information from the Mississippi Department of Archives and History.Their website has a searchable database of some manuscripts and territorial records which may be beneficial to your search.It is quite possible that they have a file on the 13th Mississippi, but I have yet to check.
I have found several references to Gen. Nixon which I sent off requests for, but none contained muster rolls.One of those sources is quoted and cited below:
“Colonel Nixon greatly distinguished himself during the war [of 1812], and stood high in the confidence of General [Andrew] Jackson.He was subsequently appointed Brigadier General, and died at Pearlington, Hancock county.”
Claiborne, J. F. H., Mississippi, as a Province, Territory and State with Biographical Notices of Eminent Citizens (Jackson: Power & Barksdale, Publishers and Printers, 1880) 1: 320.
This same source also contained information pertaining to the operations during the war, in which Gen. Claiborne took part.The 13th Mississippi appears to have operated around Perdido, although I am unfamiliar as yet with that area.Nixon was involved with securing support from some Indian tribes.
Hope this helps and I highly recommend you check with the MDAH for a search of their manuscripts.