Cutting against the grain of the last century, which was pushing he franchise wider and wider. Hard to imagine anyone going this route. Why would they, what is the gain to society?
The Canal will very much be a topic of discussion with Californie being so important and sailing around South America a gigantic time sink. Right now, 1856, it takes a year to sail to Californie from Paris! Ocean-going steamships, which are coming out now, will help but still a long way.
Not...
This is the plan but it has not happened yet. The San Francisco leadership is still arguing over issues of voting rights and such. It's complicated (of course) and will get their own updates.
Will there be a war? One of the big things that heightened tensions in OTL was the acquisitions of vast lands during the Mexican-American war, which pointedly did not happen here (mostly just Texas and then the disputed areas of the Southwest). Slavery is still a (the) major issue but it might...
This pushing it too far. California exploded during the Gold Rush. By 1870 California was the 24th most populated state. Still low compared to size, but not that backward.
Generally large scale irrigation.
I am trying to do not get bogged down in USA history, but I imagine a failed filibuster, which lead to real USA-Spanish naval clashes and then petered out when the USA was unable/willing to land troops, and then European political pressure.
Not really. Cotton was (and IS) a big product of Arizona but that came much later after slavery. Slavery did exist in OTL in those areas, but it was generally Native American slaves. That said, OTL and in this TL slave oriented leaders thought the Southwest would be prime slave territory...
Seceding from Mexico is hard to imagine but not impossible. In 1836 Juan Bautista Alvarado led a small Californio revolt against Mexico, made a constitution and their own flag. This is was mostly a reaction against a crappy Mexican governor but the revolt never really went anywhere and was...
Yes (although 'staff' in this period would be crazy tiny by our modern standards), but it is still hard to come to an agreement with a bunch of oscillating Americans. It isn't the Duke's fault, more just a difficult circumstance. The Americans were just not quite feeling the urgency at that...