Cheers! And that was supposed to read 'very very noir'. I know some of these will be spoiler-ific so understand if you can't answer yet.
1. What's the specific PoD here? Just one event or several? I'm guessing it has something to do with a certain insane mystic actually turning out not to be insane, and then meeting the Fuhrer at some point?
There are several PODs at play. One you guessed correctly; others include a healthier (from a Nazi view) interest into the development of a nuclear program, a Spring attack on the Soviet Union that allows major gains before weather turns (some Yugoslavian and Italian tweaks there) and Heydrich survives (for some as yet unexplored reasons).
2. The Cultural revolution that forms the backdrop of the story - is this like a reverse 1960s where the newest generation thought the regime had drifted too far away from the original Nazi ideals?
The defining characteristic of Nazi ideology was anti-Semitism. With all the Jews of Europe officially exterminated by the end of the War (some have survived, but on paper, all Jews were "resettled" in the East and "Madagascar"), the official "enemy" that drove the visceral Nazi hate is now a distant memory. This is causing a problem for a state with a world view built on hate. There is an awkward attempt at anti-Americanism, but much like its totalitarian counterpart of Stalinism, Nazism needs a tangible everyday visible enemy to hate. Distant America recovering from losing the War doesn't cut it in the '40s. There is a bungled attempt at hysterical homophobia. But it too lacks the oomph of the anti-Semitism and fizzles out. Though the lingering effects of the campaign manifest themselves in Inspector Brunner (a creature of his time and place) being rather fixated on male on male sex acts and the police files of everyone referencing homosexual suspicions (except for the files of the doomed Frikki, Tristan and Odette).
Running out of things to reliably hate on a mass scale, the society turns on itself. The long dormant "Socialist" quarter of the "National Socialist German Workers" Party credo rears its head and is exploited by members of Nazi regime sidelined in the 1950s. Daluege and other old timers wholly unused to running a global empire and left behind by the slick Speeresque technocrats wreak their revenge on them by using societal unrest to lead a Cultural Revolution to purify the Empire using Hitler.
Hitler by the time of the novel is a syphilitic wreck trotted out twice a year to a balcony to gaze sternly but benevolently at adoring masses. A woman gets close to him and allied with the Daluege left-behinders (and moneyed old timers too important and powerful to displace) unleashes Hell. Frenzied Hitler Youth is let loose on the Speers and successful Nazis of the Empire, with the unwitting backing of senile Hitler.
3. I saw the reference to New York - is the Reich therefore the dominant power in the world, or is there another power bloc, perhaps in the Pacific?
The German Empire is the dominant power, but US is nipping at their heels. US recovered from the war and their progress is worrying to the Empire. The Brits were allowed to keep their empire to mire them in the conflict of keeping it as a way to weaken European competition. France was allowed to keep African territories to compete with Italy, to weaken both and to force both to rely on Germany to step in and settle disputes. Japan has an Empire, but is struggling to hold onto it and keeps butting into British interests, as is intended by Germany. South America is a mess of competing powers vying for German approval, though Japan has interests there as well.
4. Latvia is certainly an inspired choice, and I liked the idea of the mystery happening in the reaches of the Empire. What less you to choose Latvia specifically?
I have visited Latvia and know it a lot better than Germany. I also did not want to set a mystery in Berlin, due to a lot of other writers doing it a lot better than me and it being a much trod upon ground. I knew I would be using a cliche divorced troubled noir detective and have femme fatales and corrupt officials and wanted to have a unique setting. Even a nightmare Berlin would be already old hat to a lot of people. A nightmare Riga, not as much. Also, having it on the fringes of the Empire allowed for delays of information from center and explain some of the sloppy mistakes made by everyone involved. If they were right by the nexus of power, it would be a lot harder for people to escape attention. I also did not want Daluege to take over the story completely, as he would have, if the action took place in Berlin or even Vienna. He is supposed to be the straw that stirs the drink, not the drink itself.