Would it be possible to get a world map to see all the differences so far?
Alas I've been plinking away at one for 1866, but just haven't found the time to finish. I'm using a different laptop which doesn't run the same programs now, so I'm trying map making from scratch.
I may dig out the old dinosaur which had many of my tentative maps and make one, but I'm going to design one for 1866 and 1872 so people can get a good look at the world. Eventually...
Without Bismark you lose one of the main agitators for the Franco-Prussian war and with the 4 wars of German Unification you could just see France in the background just eating popcorn while their main potential rivals on the mainland just beat each other up.
So the first was seen as happening in 1848, this is the second in 1866. The next two will take place in the next decades (so before 1950 if that helps). But I think France can't not help itself by getting involved. A stronger Prussia, which the North German Confederation definitely is, is something no French state wants. Couple that with an Austria who will probably be more belligerent, and you have a recipe for disaster at some further point in the 19th century which may or may not lead to some even further disaster in the 20th!
With Italy losing the war and Prussia not growing in strength would the French be more willing to defend the Papal States?
On that you can definitely count. Keeping the support of both the clergy and the Catholics of France as a counter balance to the liberal politicians is going to be a must going forward, and not just because the Empress was partial to ultramonte politics. So the temporal power of the Pope is going to endure well beyond 1870.
Having Four Wars of German Unification is something I did not expect along with Bismarck, Moltke, and Wilhelm dying. Is one of the four wars going to happen in the Great War? Given the next 50 years would likely not include the other two wars unless they happen so close to each other, I think that is likely. It brings up the question of what the sides are in the Great War, whether it is two alliances at war a series of alliances that are allied to each other and fighting all over the world, or a series of regional wars happening roughly around the same time and are collectively called the Great War by future historians and politicians (although that last one seems unlikely and way too messy to keep track of).
Given that you want to avoid 'Turtledoveism' and based on the 'What If' chapter, I guess that means the Confederacy will not participate in the Great War as they deal with massive internal problems.
There's some stage setting for later conflicts here in the 1860s we've seen already. The powers of Europe are going to be adopting massively different priorities in the coming decades. Some are going to put them at extreme odds with one another (and Asia is going to be a particular sticking point) while some will pursue alliances because they have no other choice.
Friedrich as king of Prussia could mean a future Germany becomes allied to Britain against an alliance between a stronger Austria and France in the Great War. Not sure about Italy but they could be pushed into the British camp. Not sure where Russia falls in here as they look to be focused on their Asian possessions.
I couldn't possibly say
I am not sure if two of Britain's economic and political rivals (the US and Germany) are knocked clean off the chessboard because of these setbacks. The first chapter did say the US would become a Great Power. It would likely be an economic hegemony in the Americas along with other nations like Argentina and Brazil (which I predict will be Great Powers) that Britain would also have to contend with. Germany can still be a significant contender in Europe although likely not against Britain if they are allied in the future against a stronger Austria.
As said upthread, both are still going to be major economic powers, with now slightly truncated goals for the future. The US between, oh, 1865 and 1890, is going to be more immediately concerned about what is happening at home and giving itself muscle and political stability. The rise of the New Men is going to really change up American politics and priorities.
Prussia through the reign of Friedrich is going to be thinking about things a little differently, as Friedrich was very anti-Bismarck so consider that an important factor. However, when he dies, Wilhelm brings in a whole new game. The 1890s will be big divergences all around the world.
Lastly, for a Year in Review about things happening around the world, there are still no notable changes in Africa although I'm sure the different history of Germany means that at least there will be no German Togoland and Kamerun. There's barely anything about the Ottomans other than suppressing a revolt and alienating some parts of Europe but I guess that would be for the 1870s.
Nothing earth shaking in Africa yet I'm afraid. My own knowledge of what could change is rather limited, and will probably keep the big changes for the next three decades I'm afraid.