3. The longer term trajectory of the Confederacy. From OTL we know that much of the south later had significant value due to oil wealth, but that's not going to become significant until 1895-1910ish. And we've got a lot of factors with potential to play to the Confederacies' determent in the meantime... the dominance of cotton (between first the Union blockade and the 'current' conflict between the Rebels and the Poms alternate sources will be sought, possibly badly knocking down the South's revenue in the 1870s and 80s); the ongoing (well deserved and likely increasing) stigma arising from slavery (I severely doubt the South would consider abolition for at least a generation post-war); generally limited industrialization; existing breaches between the plantation owners and 'poor' whites (wonder if that could actually drive emigration from the CSA to USA...); lack of development of inter-state infrastructure due to various hardline states'-rights nuttyness. Hell! Ongoing issues from those will likely see any oil boom drastically cut back... if not turn the Confederacy into an out and out Banana republic (heh, that could be funny... Florida or Texas as the target of filibustering instead of various Central American states...). It could very well be that ITTL a Yankee's opinion of the South circa 1900 will be less grumbling about lost territory and more "I'm glad we're rid of that cesspit"...
The other elephant in the room is that states in the Confederacy will have the established right to secede.
So, when there is a disagreement between a state and the Confederate government, the state can simply leave.
Imagine Texas seceding...what happens to the new states/territories west of it when they no longer share a contiguous country with states to the east?
The CSA is an intentionally weak government, held together by the exigency of the external USA threat during the ACW.
How much will its states be willing to cooperate and contribute beyond the national defense level?
Its an interesting experiment in local vs. national governance.
Most immigration will be into the remaining USA as, similar to OTL, that's where more wealth and opportunity lies.
Will states in the USA also see a precedent that they can secede?
What happens when a USA state decides to test this?
As for the USA getting along with the Confederacy, Turtledove's general trajectory in the
How Few Remain /
World Wars series seems most plausible.
Whenever Europe fights a world war, most likely so to will the USA & CSA since they're unlikely to steer clear of entangling alliances.