Stephanie,
I do not know anything about the ticket system, so hopefully someone else can help you.
As to pulling the sword out of the stone, well...
When you ride the two new rides, you randomly get a new one-time use magic pin, Sword in the Stone magic. You put it on, as you do with any magic pin, walk over to the sword in the stone, say a quick prayer, beg, whatever you want to do, and say, "Draw!" (or you can double click on the pin from the magic wand menu). If you are extremely lucky, the sword will rise up out of the stone, and you have yourself a new tea cup pin.
If you are like the rest of us, you get a message to the effect that you don't have what it takes to take the sword out of the stone, try again.
Between Tuesday and Wednesday evening, using two to three characters at a time, I received about 25 magic pins. I pulled the sword out once. Others have gotten the pin the first ride through then pulled the sword out right away. It's all random, kind of like the Jack Sparrow costume.
Good luck.