Apartheid South Africa would inevitably collapse since the black population outnumbered the whites, in the CS the majority of the population is white which means that segregation wouldn't be a problem to put in place, I don't know about the US segregation a lot but it would probably be a similar thing.
US segregation relied on a combination of Northern apathy, normalization of racism among the Northern populace, political deadlock by a united bloc of Southern white supremacist politicians, and
herculean amounts of state maintenance of segregation. Like, it genuinely took
massive amounts of work to maintain white social buy-in to the norms that allowed the white supremacist structure to be maintained, and to maintain the structures themselves. Even then, there were continual efforts, even if halfhearted, to implement civil rights guarantees throughout the post-Reconstruction period; the Lodge bill of 1890, for example, would have effectively ended segregation, but was traded away by Northern business interests and Western farm interests for their pet projects (and then caused a rift between President and Vice-President that definitely didn't help in the 1892 elections).
That is different, France got humiliated and was fueled by revanchism and the Germans didn't hate the French; people will probably blame Lincoln for everything and go back home as nobody would see a point in going for round two.
And the US wasn't humiliated in this context? Keep in mind that >100,000 Southerners fought
for the Union, complete with two separatist movements in CS states (one successful), and a significant rebellion in Mississippi following the loss of CS control over the Mississippi river. Support for the war was pretty solid from the Republican majority in the North throughout the war. More likely, the secessionist traitors would become the focus of American national hatred.
Mexico is kind of easy to integrate as the Second Mexican Empire would survive with help from the Confederacy and be a puppet and integrating the Cuban elites into the Golden Circle won't be very difficult
...No.
Just...no.
The Second Mexican Empire was an unstable joke that imploded almost immediately after French support was withdrawn. Integrating it would be very difficult (the elites were already unhappy with Max, who was too liberal for their taste, the common folk would never accept a foreign backed king, and as others have noted Mexico is EXTREMELY difficult to control due to its large central mountain belt and dearth of easily accessible ports), cession of territory would require military conquest and significant investment in pacifying a fanatically hostile population accustomed to guerilla warfare, and a recovering CS would be in no position to seriously attempt that.
The French were humiliated and faced diplomatic isolation, the why would the US citizens want to die for a territory that clearly doesn't want to be a part of them.
Over two million men were willing to die for a territory that had seceded. Look at their surviving letters, those might shed some light on why they chose to sign up to fight for Lincoln and Liberty.
While I agree that Spain isn't going to give up on Cuba, in the long run the CS will certainly be able to surpass the dying Spanish Empire in naval and military means.
With what industry? With what allies? With what ability to counter US power projection? The CS could barely slap iron cladding on hulks, the leadership was ideologically opposed to industry, they would not have the capability to take and hold Cuba.