"Do we need to split up the United States into separate nations, or
at least make a group of smaller states into one collective? I don't
really like the idea, but seeing as how different Texas is from, say,
Connecticut, who says the idea wouldn't just be a formality now?"

The US is 50 states [50 nations]- btw not 57 as Obama said.
What is needed is for the Federal govt to be granted less authority and thereby return this to the states and local govt.
The power of each state then can be checked by other states being a choice that citizens could decide to move to.

"If the CSA had "won" in 1865, would either the CSA or the Union still exist by now?"

Probably, both would exist. Question would CSA still have slavery and if so which side would CSA have picked in WWII?

Would CSA have taken over Cuba, how about Mexico- or South American in general.

It seems with America divided, we would not have won WWII. Japan attacking Hawaii would be attacking either the Union or CSA.