The answer if Credence is really Aurelius Dumbledore or not?
Some fans already mentioned that he couldn't be a direct brother of Albus, due to Credence's age in relation that Percival (Albus' father) was already in Azkaban and (Kendra Dumbledore) Albus' mother already being accidentally killed by Ariana, by the time Credence had to be born. A cousin or something appears more likely if Credence is really a Dumbledore. The Phoenix could be Fawkes, due to the mythical rule about only one phoenix being alive at the time. Of course Rowling is free to break that rule, and it's also said that Fawkes grants his loyalty to those or deserve or really need it, and in some ways both Credence and Albus can fit the bill in some way.
Also take a note of the man who told Credence that he was Aurelius Dumbledore. That was Grindelwald in person. How could he know? Also we do know that Grindelwald is a man who deceives people, and who has a bone to pick with Albus. Putting Credence up against him (since Grindelwald cannot hurt him directly due the the blood pact, and possibly he may not have notice Newt's Niffler stealing it) by lying about Credence being an outcast Dumbledore is something he would do.
Now what Grindelwald and Voldemort had in common is that they traveled the world. So Brazil doesn't seem so strange to me. Voldemort spent a lot of time in Albania.
My big question is the question if Credence is actually a Dumbledore or not... Rowling is known for her mathematical errors when it comes to time measuring, so Credence still could be, but at the same time, knowing the lies of Grindelwald... Anything is possible... Like we're used to see...