DISCLAIMER: If you haven't seen the movie The Prestige, stop here and do not read this thread. This is a response to a post in the movie thread, and I started a new thread to avoid hijacking the other one.
My interpretations from watching the movie is that once Tesla put his finishing touches on the machine - he made several references in this nature of needing to work out the problems - the machine then either 1) transported the original Angier to a new location, or 2) cloned a new Angier to a new location while the original Angier did not move (I'll get into this more at the end on why I feel it's #1 instead of #2).
During each of Angier's performances - IIRC, he agreed to do 100 performances - either the original Angier or the cloned Angier dies each time. Once the cloning finalizes in the machine, a door in the floor opens and the Angier standing in the machine drops into the water tank. Whether this is the original Angier or cloned Angier that drops into the tank, I do not know for certain. Anyhow, the Angier that drops into the water tank during each performance drowns, and Angier hired blind stage assistants to help remove the water tanks after each performance. In essence, Angier knew that he couldn't have several cloned copies of himself existing so he had to kill the double (or himself while allowing the double to live) after each performance without anybody else knowing (that is important).
Now, to your questions specifically on Angier ... the Angier that you see on the autospy table is the Angier that dies during the performance that Borden witnesses when he runs below the stage. Since the Borden twin who witnessed the drowning made a spectacle of Angier dying, other people suddenly knew that Angier apparently died ... which forces the living Angier to disappear under a new identity of Lord Caldlow. Society and law enforcement officials at that point believe that Angier was murdered by Borden, and that's why the one Borden twin was charged with the murder on circumstantial evidence. While the one Borden twin is in prison, the other Borden twin is disguised as Fallon at all times.
The Angier that you see in the water tank during the movie's final scene is one of the many Angiers that died during his performances. His blind stage assistants used that warehouse as a storage facility for each water tank, but it's also important to know that the blind stage assistants had no idea there was a corpse inside.
In the movie, Cutter held an allegiance to Angier all the way throughout until he realizes that Lord Caldlow is Angier during one of the movies final scenes. This much seems clear to me; Cutter's allegiance shifts to Borden when he realized that Angier stole Borden's daughter.
Back to the original Angier vs. cloned Angier ... the movie doesn't appear to directly tell you which Angier is transported and which lives, and it gives hints that it could go either way. First, after Angier is shot by one of the Borden twins, you see a flashback to when he first used the machine. A cloned copy is produced outside the machine, and the original Angier picks up the gun and shoots him in the chest.
However, Angier also has a strange reaction near the end in regards to killing his clones (or dying himself), and it may or may not be a stretch for new cloned Angiers to understand how many performances he's done in the past. Remember the story Cutter tells Angier during his wife's funeral to ease Angier's pain over his wife's death (i.e. he had a friend who described passing away as "going home"). At the end of the movie, Cutter tells Angier, "I lied. He said it was agony." Angier's reaction to that is a bit strange. He tells Cutter that each time he stepped into the machine, he never knew if it was going to be him or the clone that would drown.
After typing that all out, I realize this may confuse you more than ever. As it is, the movie really did fascinate me, and it's one of the best movies I've seen in quite a long time.