Question: Why was the playfair cipher on the missing page invisible? Thomas Gates wrote it in normal ink.
Chosen answer: Thomas Gates didn't write it in normal ink. He wrote in pencil. The cipher wasn't written on that page, it was written on the facing page and minute bits "transferred" onto the page with the names.
Question: How does finding the treasure clear Thomas Gates of plotting Lincoln's death?
Chosen answer: Because it verifies the story that the Gates family has passed down, that the pages were burned to protect the city of gold's location, not to hide his name as a plotter.
Question: What did Ben Gates know about Mitch Wilkinson that made him know that Mitch "NEEDED" to find the City of Gold?
Answer: It wasn't that Mitch knew anything about him, just that like himself family history was very important to him. Mitch needed to find the city of gold to redeem his family name in that it was his family that was traterious in the past not Ben's.
Question: Why was Thomas Gates' name on that page?
Answer: Gates' name was added by Wilkinson to get Ben to do all the work in finding the treasure (as that would prove Thomas's innocence).
I disagree, Gate's name was always on the page. Presumably the investigation of the page would have revealed that it was a recent addition not a contemporary part of the text if this were not the case. Perhaps a simpler explanation is just that the conspirators needed to consult gates due to his deciphering skills, hence his name on the page, which explains the name "mastermind" as well.
Thomas Gates was on the page listed as "Artifex" which just means a practitioner of a craft. Mitch tries to say it's a "mastermind" but that's not 100% true, it could be but also just an expert at something. The museum curator who says, "we'll have this authenticated" was paid off by Mitch, so Mitch could very well have added the name and the curator lied.
Mitch says in the movie that adding Thomas's name to the page was the only thing he could think of to get Ben "in on the hunt." He says it at the end of the movie when he is apologizing for smearing Ben's "great great granddaddy's" good name.
Why does finding the treasure prove Thomas Gates' innocence anyway?
Question: Why does the president ask Ben to look for the page 47 of the book for him if he, as president, has access to the entire book?
Answer: He asks him to investigate what's on page 47, not to just read the page.
Question: Why does Ben need to find the city of gold to beat the kidnap charge? The President's story of "We got trapped and he saved my life" would work just as well without the discovery.
Answer: Ben lured the President to the tunnel to ask him about the Presidents' Secret Book, knowing the President wouldn't admit its existence in front of anyone else. This also means the President couldn't tell secret service what really happened. Ben told him he needed to see the book "to lead us to the discovery of the greatest Native American treasure of all time." The President doesn't know if this is true or if he has some other criminal plan for the book. Finding the treasure shows the President that Ben was telling the truth. Had Ben been lying, the federal charge of kidnapping the President would put Ben in prison for life, effectively punishing him for the kidnapping as well as for lying to the President. Considering Ben had already discovered a massive historical treasure once before, and knowing the recently tarnished name of Ben's family, the President was willing to trust that Ben wasn't lying about his intention and gave him the information needed.
Question: In the legend of Cibola, the ship landed in Florida. Why did they show him the City of Gold in South Dakota? In those days for an entire group of people to travel that far (on foot) would have been deadly.
Chosen answer: You (or the movie) have your legends confused. Cibola was supposed to be somewhere north of New Spain (now Mexico). The Spanish conquistadors explored much of the southwest looking for it. Coronado travelled from central Mexico all the way to the northwest of Kansas and back (without dying!) looking for Cibola and Quivera.
They mention he wrecked off Florida but when they find the city it's under Mt. Rushmore which is in south Dakota.
Question: At the end of the film there are a bunch of people in the lost city of gold. If the devices were busted up and didn't work any longer, how did they get the water out? Also, if there's not really a way in any more, how did they all get in?
Question: Who was the Native American corpse with the knife in his chest that Wilkinson saw after climbing the ladder inside the cave?
Answer: It's impossible to know. Presumably, we are simply meant to assume it is a random Native American and no-one of significant importance.
Answer: It is never explained what was on the page. It was just a cliffhanger to set up for a 3rd movie, I think.