To answer all of your questions, this is going to have to be a tl;dr. Brace yourself.
As for your first question, on how to get Mewtwo, you first must become the champion and beat the game. After that, go to the Pokemon Village off of Route 20. Once you are there, surf to the cave near the center of the area. Inside the cave, you will find Mewtwo.
Note: Mewtwo is Level 70. Brace yourself.
Now, your second question. You get the Mewtwonite X/Y by defeating/capturing Mewtwo. The item will be in a Poke Ball. Interact with it and you receive the Mewtwonite.
As for your 3rd question (which is unrelated to this), the Torchic Gift has not expired yet. It ends January 15th, 2014. So get it while you can!