Q1: Saving your deck means copying your deck code somewhere, like a txt-file. This is just so people can look over it for a legalty check. However, do never post them officially before the tournament is over!
Q2: You go to PvP Duel, type the in-game-name of your opponent, and hit "Go!". Then, it is just as every other game. Keep in mind to take a screenshot of the winning screen, if you won a game.
Hint for PvP: Keep the game in its own window of your browser. If you have it in a tab, changing tabs can cause desync errors, ruining the game. (You can test this when rolling after winning against an AI and then changing the tab, realizing the slowed sound.)