I decided to solve the puzzle by playing the game rather than researching the storyline. I love the game of chess, thanks Dad for teaching me early in life, and so it was a natural choice, but you may wish to play the game since the only official hint given in this quest was to do just that. If you need assistance with any of the challenges, or if you have questions about any of Google's products, services, or API's, you may leave your email in a comment and I will be happy to assist you.
Oh right, you wanted the answers to those questions so you don't have to play chess. Since you can't be persuaded otherwise, here they are.
"What is the spiked belt that Silas wears called?" A cilice
"What are the second, third, and fourth leading members of the Priory of Sion called?" Senechaux
"The engraved tablet that is supposed to reveal the hiding place of the Holy Grail is called the" Keystone