1) The reason why the SW ended up in the DSA in-TL has to do with Texas going independent from Mexico and establishing its own republic (while owning said New Mexico-SoCal bits in the process, see
here). When Texas got rolled into Southern America by the end of the Slaver Revolt, those western parts came along for the ride, since there's no reason to just give them back to Mexico without compensation at that point. And keep in mind, Mexico in-TL had no say in whether Texas could have NM-SC or not, they had several secessionist movements to deal with at the same time (including the Yucatan and all points south). At that point, those territories taken by Texas were no longer Mexico's to give in any meaningful, practical, enforceable way.
2) Not really, Baton Rouge was tiny compared to Charleston/Savannah during the early 19th Century, and thus had less demographic sway on political events than the latter two (not to mention that the TL, AGAIN, addresses this by indicating how Loyalist sentiment got stronger the further west AND inland you got, which puts Baton Rouge further from Confederationist safe-territory than you'd think).
3) Or American....after all, it was New England Yankees that filibuster'd the place in OTL, no reason why that couldn't/wouldn't also happen here either (especially if the rest of the Americas' resources are seen as off-limits due to the British/DSA standing in the way).
4) Why would the DSA care if the black population increases? This is well before the advent of Jim Crow (which in many respects was a unique by-product of the Reconstruction period of OTL, which wouldn't exist as we know it in TTL) in terms of encouraging African-descended people to leave, and the arrival of non-slave Indian labor means a different "other" with an alien culture arriving as part of the work-force, unlike Black Southerners which by that point are a known factor in the region. Why would the Caribbean see the mainland DSA as unfriendly, if the money flows just as it had before (and in OTL, Britain's brief control of Cuba after the Seven Years' War saw an uptick in economic health vice the stranglehold that Spain favored by that point in time, any reason why this wouldn't also happen under more permanent conditions is counter-indicated)? And just because there's still a flavor of racism in the DSA doesn't mean segregation exists either (which I REITERATE was a by-product of the immediate post-Civil War in OTL, and the Slaver Revolt is actually quite different in many important respects from that conflict, so that analogy as an indicator of follow-on events doesn't work).
5) Quite.
6) That's a lot of high-detail speculation that doesn't have a lot of context supporting it, to be frank. That being said, using Canada as a baseline and then extrapolating relative assets using the increase in manpower, GDP, resources, etc. seems like a safe enough process. Knowing what we do about the Global and Population Wars helps form a few formative principles;
- The establishment of a standing army using the Permanent Militia as a basis, which means a robust active-reserve dichotomy like OTL Canada. Doctrine likely based around mechanization (though perhaps lacking in dedicated heavy armor units, due to the next point) and use of long-range raiding tactics due to the cavalry tradition in the OTL South/Southwest and use of irregular forces during the Slaver Revolt by both sides, and against Mexico during the Global War.
- Construction and crewing of anti-torpedo boat ships (aka destroyers) + ongoing trade and transportation to Britain during the Population War means a probable green-water navy instead of a brown- or blue-water one. Thus, no supercarriers, but a possible amphibious capability and a decent surface fleet. Stronger than the RCN, weaker than the USN, close equivalent to the Australians or Dutch by modern day at a guess.
- Absolutely no clue about the Air Force, but considering the course of the Population War we can reasonably expect there to be no bomber community, probably a focus on transportation, patrol, and battlefield air superiority/CAS. Equipping aircraft would probably be a mix of British, American, and domestic (again, using OTL as a basis).
7) Most of Canada is tundra and taiga with huge variances in annual climatic conditions; that severely limits its ability to extract minerals and agriculture from a huge bulk of its territory (to be fair, that gets better as technology improves, but does stunt initial growth potential). The DSA doesn't have that problem at all, the majority of its territory is accessible due to more conducive climate (especially since air conditioning isn't as big an expenditure as dealing with a quasi-arctic climate for much of the year, let alone the wear and tear of the geologic makeup of northern Canada on drilling equipment and the like vice the SE/SW of North America). And that's leaving out the agricultural component of both the continent and the Caribbean islands, which makes a HUGE proportion of British cash-crop potential. And a bigger population means a larger work-force.
8) Perhaps, but it's entirely up to Britain to listen or not. And I'm not sure they'd give a whiff about what the ex-rebels have to say about the matter. Using "Carolina" as a title at least has historical precedent backing it up, whereas Georgia/Florida/whoever doesn't have that extra credibility as far as titles go.
And speaking for myself, it's less that this isn't interesting as a discussion (I've wondered some of these things myself), and more that it's a lot of speculation from a "blank sheet" without the OP's input, which makes it a rather moot discussion.