Always go first:
Save the game in front of someone, then duel them. If you lose the coin flip, turn off the game and go back to where you saved. Then, choose the opposite of what you selected last time. You should win, and be able to start first.
Level 3 Nature Deck:
Enter FOREST as a name to unlock the Level 3 Nature Deck in the preset decks.
Completion bonuses:
Successfully complete the game to unlock Duel Room in the main menu, and Image Gallery in the Cool Stuff section on your pocket gizmo.
Third Starter Deck series:
Win the shop tournaments in a town five times to unlock
the corresponding deck.