“Jackson was a very odd bird” is putting it mildly. Brilliant though and drove his men even harder than Patton. Had he been at Gettysburg the CSA might have extended to Brazil by 1900.
Speaking of Gettysburg. How different things might have been in Jeb Stuart had not been on an extended sortie.
Very unlikely. Southerners with this dream weren't thinking it through.
Given the transportation technology of the time, conquest of Mexico, Central America and southward could only be accomplished by sea, as indeed the American conquest in the Mexican War was, after an overland attempt had failed.
For over 50 years a British commitment to opposing slavery had been fundamental. The Royal Navy (not to mention the US Navy) might have had something to contribute to the discussion over whether the CSA would be allowed to conquer its way into a slave empire in Latin America.