Somthin about Armenians not being left alone?
Armenian massacres took place, in OTL, in 1916.
Does the PoD have something to do w/ the Ottoman Empire?
The PoD itself... well, very, very, very, very, very indirectly.
What's that gold nation on USA's southern border?
The North Mexican Confederacy, formed by some yet another revolutionary, like say Pancho Villa.
And why does Russia have large swaths of Manchuria and Mongolia and...well, damn-near half of Asia...
They actually did hold all of Manchuria in OTL for a while. As for Mongolia, it was often as good as a part of Russia anyway.
Something about the Great Game leading to a Russian invasion of Persia, and retaliation by the British and their Ottoman allies?
Briefly put, no. But you did guess some parts, and horribly misguessed (is that even a word?) in others.
What "Axis"? The year is 1910 right now.
reconquering half of Persia, the Ottoman Black Sea coast, Mongolia and Manchuria from the Chinese who apparently supported the Entete, and invaded India. They were only stopped in the southern front by massive British involvement.
Persia was reoccupied AFTER the war. As for Ottoman Black Sea coast (and indeed the war start), see Amen's first guess. I already said that this started WWI - read more carefully.

Either way, they captured it. China supported Britain indeed, and were beaten up, and Russians did invade India, and were, along with their native allies, stopped by the British.
The Austrians for their part were not invaded by the Russians, and managed to hold their empire together for a while, but fell apart either late in the war or after it.
Oh, they were attacked by the Russians on two fronts, but this strenghthened the Hungarian support for the Hapsburgs as opposed to the pro-Russian Slavic rebels. The Austro-Hungarians were forced to grant independance to Czechoslovakia and a lot of land to Serbia/Yugoslavia.
Germany did not succeed on their front, mainly due to massive American involvement as early as 1915 (see below)
Note that the MAP is 1910.

They did not suceed on their front, but the Americans were too busy dying in the trenches of Cuba...
their allies the Russians who made peace
Russians weren't German allies...
a Communist-type revolution.
A National-Communist revolution. Its a different thing, if not altogether.
The French annexed Belgium and Lux. as part of the peace because they wanted to make sure Germany couldn't invade, or these were annexed in some earlier war.
Well, it was a part of the peace admittedly, but that pretty much was a recognition of what it was de facto.
Thus Zaire became one of the first states to gain independence in Africa.
Nah. Its the Congo Free State. Remember what was the Congo Free (E)State?
Mexico joined the Axis, because they thought with Russia aiding them, it would be an easy victory. They were wrong, and Mexico apparently was split in two, perhaps by American involvement, with much of their territory directly ceded to the American giant.
Nah, Mexico remained neutral, but suffered from an earlier civil war in which USA intervenned, partially to test out new, post-Cuba military doctrines.
Pakistan was probably a Russian puppet state or simply a buffer state between India and Russia as part of the peace that ended World War One.
Yeah, a puppet state. Only its called Sind.
Why Sweden still hasn't given up Norway
An earlier World War One, including a lot of bluffing and ultimatums from both sides against poor Sweden-Norway, tends to alter its political history to prolong the unity.
why Suriname is apparently not owned by any human nation, or at least none with a capital
Uh... Lizards from Turtledove took over it, concerned by the sudden change of history and universe-blowing-up consequences of it. Or perhaps I just forgot to change the color to the Dutch one he picked for his 1914 map, whichever explanation you like better.
how the Italians apparently won at Adowa or as part of WW1 conquered Ethiopia
They conquered Ethiopia AFTER WWI in which they did considerably better and as such suspected they might stand a chance against Ethiopia this time. Against common wisdom, they did indeed win the "Adowa Rematch".
They occupied it during the earlier WWI, which took place before the French conquered it. They didn't want to withdraw from it afterwards, and the French didn't really want it THAT MUCH.
That scenario also does not explain why Liberia, Cuba and Panama are all directly under American control.
Reluctance from my part to add any more states does, though. I actually do have a good explanation for Cuba part, as the "Cuban", or "Spanish-American" War was much more bloody then in OTL (the Spanish were carefully studying the early moves of WWI, and adopted some of the tactics agianst the more isolationist Americans), the Americans were more reluctant to let go of it. I think you can suppose that Liberia requested American protection after some war-time border incidents, and the same goes for Panama, though in this case the Americans had played a large part in them requesting that, afraid that the British might seize the canal after a rather nasty war-time incident caused quite a stir in British newspapers.
Another hint: It had something to do with a government change.