I know that American Civil War alternate histories are over used now these days, but how would a Confederate government and it's departments and military function in the early 20th century?
This has been done a lot...but short answer - weak central government, no rights for blacks, female suffrage very far in future. Limited "federal" army, although navy federal. Army units based on a national guard type system, but central weapons purchasing etc.
I have my doubts the Confederacy would have a weak central government. For the time period they existed in OTL they had a stronger one than the North out of military necessity. That probably wouldn't change after the war.
They probably would've ended slavery by 1900. Women's Rights might be a thing in the early 1900s,Desegregation may occur later in the 70s or 80s though. I imagine they would've had to strengthen their Central Govt or risk all their members succeeding. In OTL,Georgia was already considering succeeding from the Confederacy before Sherman's March.