The revolution caused Sophie to lose a few pieces of her mind.She immersed herself in the culture of Paris for ten years, gaining a French accent in the process, in large part to drown out bad memories. There were also a few other pieces of her mind missing before the revolution. Dowager Empress Marie knew this and kept an eye on her. This, however, is not crucial information. Think about it: Soph had to have strength to have escaped the palace and country, so her peculiarities are (at least as far as the movie plot goes) irrelevant. Evidence and mentions of all of this can be found in the original script which is floating around the Internet. It's basically the same as the movie script we know, but extra bits and characters (such as Sophie's sisters, her opposites) were cut for time.
Sophie is Charlotte's mother.The timeline is fairly close, they're similar in looks, and Sophie's (presumably) French. Now there's just ignoring the different studios bit.
It all is a daydream the real Anastasia had.The real Anastasia was still a child when she was shot. It was a dream she made up to keep herself happy, about marring a handsome con artist, having her family be safe, wear lots of nice clothes, live happily ever after like in a fairy tale. She was probably too young to realize why she and her family were being persecuted, so she made Rasputin, a friend of the family, the magical villan.
Sophie is the second chance of Marina Del Rey. Vlad is Benjamin the Manatee.Watch both Anastasia and Ariel's Beginning with this in mind, and tell me you don't see the resemblances. Marina even had hair of Sophie's color before it fell out. As a bit of trivia, in real life, Sophie's character's inspiration was governess to the Romanov daughters before the revolution, just as Marina was governess to King Triton's daughters. My theory with the animated worlds is that someone believed Marina deserved a second chance at happiness and living a spirited life as opposed to rotting in jail or whatever her final fate was (even if she did become Ursula, which is something people have split opinions over). The mermaid movies end right around the time Vlad and Sophie were born, too. Perfect time for reincarnation.
The movie takes place in an alternate universe/scenario for the Russian Revolution.This one should speak for itself; in an alternate universe, Lenin and the Bolsheviks managed to not only take the palace down in one revolution, but also managed to have the Czar and (most of) his family killed. In this universe, there is no "October Revolution"; only the February Revolution. Furthermore, in this universe, Rasputin is responsible for the Bolsheviks' takeover, and has supported them from the beginning; he provided them with the funding, spread the word of their cause (maybe he was the one who put up the slogans everywhere), and took over when Lenin was in hiding (possibly receiving Bartok as a present in return). The Czar somehow found out about this, and this was why he called Rasputin a "traitor". Rasputin took this as an insult, as he genuinely thought that turning Russia into a communism would help the country and therefore the Czar should be in gratitude. Angered by this, he finally decided to give the Bolsheviks the signal to attack, and used his little green pixies to help them get in through the gate. And finally, Anastasia was born several years later, which is why she is a child rather than a teenager when all this happens. Of course, these events all contradict the actual timeline, but when you place these events in an alternate timeline, it all makes sense—the movie is going with that timeline instead of the one in our universe.
Pooka is some type of angel puppy.Anastasia asks for a sign, she gets the dog. Pooka is the one that points out the explosives on the train. Pooka is the one that woke up during the dream sequence to point out she was missing.
Bartok is a folk hero in this universe, and his movie is the story in question.That explains the anachronisms; it's a 18th-19th century retelling of an old fairytale, or a child's interpretation thereof, and so blends in elements from every time period up to then. Which also explains why he'd end up as a familiar to someone so Obviously Evil. In the first movie, Bartok is either summoned from a "fairytale world" or a homunculus created in his image and personality. After all, who better to serve as an ally then your universe's equivalent of a Chessmaster Sidekick?