I am not sure there would even be a CSA in the same form it took upon secession. It was a country based off of, and filled with politicians who were strong supporters of states rights versus the central government. With the precedent of secession having been set, it is likely that sooner or later, one state would decide to take it. There were signs of this emerging in OTL even when the war was still going on, with time it would only get worse. Especially because its economic prospects were nowhere near as bright as its northern counterpart, even if it did not cling onto slavery. Its also very possible that they could be defeated if there were another war with the USA, or even Mexico, seeing as they would have only won independence through a combination of luck and good military leadership.The CSA could have simply split into a collection of independent states, with some possibly being reabsorbed into the Union.
If it somehow survived all that, I think it wouldn't be regarded as anywhere near economically prosperous as the the USA or Canada. Mexico is probably the better comparison. Civil war or military dictatorship is not out of the question. As for slavery, they would likely cling on it for longer than most, if not all, other American countries, but eventually it would be forced to drop it under international pressure, probably in the late 19th or early 20th century, though you could see some kind of segregation system last for sometime after, perhaps ending around the same time as apartheid in South Africa.
When it comes to WW1, I take the view that some major European war was very likely after German unification, which I doubt a Confederate victory does anything to butterfly. It might not be recognizable to the war of OTL, fought in completely different ways with different countries on each side, but it would happen. Whether the USA and the CSA get roped in is more open to consideration. I would have my doubts that the CSA would allow itself to be entangled in a war with its vastly more powerful northern neighbour, though.