Abolition might not pick up steam again until the early 1870s and by then Kentucky would be pretty safely in the Union and likely not in a position to secede. With the defeat of Lincoln, the Union cause, and the Republican Party the first thing the abolitionists are likely to do is start squabbling amongst themselves about why they failed just like any other ideologically-motivated movement that suffers a serious blow. That coupled with the likely negative perception in the general public (abolition was NOT as popular as the modern conception of it was, a lot of the draft riots were motivated by NOT wanting to fight for the freedom of the slaves) of the abolitionist movement that pushed them into a losing war that divided the country and killed thousands of good young boys. Slavery probably will continue on in the Union slave states more due to lack of action than anything else and eventually whither on the vine as the lack of the internal slave trade or sources for new slaves whither and likely more run away north either to other US states that are free, west to where their owners can't catch them, or further north into Canada. Without a powerful slave-owning bloc in Congress the best the slave states can hope for is being able to keep the institution intact. Kentucky could also be kept in if the Unionists play it smart (assuming there is a plebiscite of some kind) and play a populist campaign against the wealthy slave-owning minority. Contrary to popular opinion there was quite a bit of of resentment and opposition to the war in the South among the poor and middle class for economic reasons and dislike for the power of the plantation aristocracy.
As another poster noted the North is likely to be much more industrial and I'd bet the bulk of immigration in the later part of the 19th century that does go to the US is still going to go North. In the South you'll have slaves or, assuming the South has its arm twisted into emancipation by Britain and France, something similar to apartheid keeping blacks in the same place. This eliminates the possibility of poor immigrants carving out a niche as cheap, unskilled labor since that is already filled by slavery. Immigration might not be as extensive as it was OTL but the bulk of it will definitely head north.
As for long-term the CSA is going to have to industrialize to keep up with the Union. I'm betting more intelligent plantation owners are going to get ahead of the curve and put their money from cotton into moving into industry and use slaves for the mass labor. We know from previous examples in the early 1800s that slaves were used in some industrial projects with success so there's no reason to think that wouldn't be attempted later on larger scale and it wouldn't work. If you have enough plantation owners making the switch then you might end up with a wave effect taking place with the fence-sitters jumping in. Economic power is likely to stay more stratified in the CSA compared to the US, there will definitely be no Andrew Carnegies in the CSA when all the capital to start an enterprise is tied up with the planters/factory owners who likely are going to develop and keep a pretty plush aristocracy to keep themselves in power. The government will be more oligarchic in nature compared to the US with race being used to keep the poor and the slaves at each other's throats instead of going after the people on top.
As far as Confederate expansion, if it happens, most likely it will be in the Caribbean first and will need the CSA to build a real navy. Don't expect anything until at least 1872 (two terms after the war began, enough time for that kind of shift in priorities to happen). As far as the European wars of unification once Bismark gets his war with France, and somehow he will considering he was able to take a peace conference OTL and turn it into a national outrage, then you'll see the unifications of Italy and Germany more or less as OTL. If you have a CSA friendly to Britain and France, a USA still friendly with Russia, then odds are you might end up with a stronger Three Emperor's League later turning into a real alliance with the USA, Germany, and Russia as the main heavy-hitters. It would also likely lead to closer relations between Britain and France sooner.