To erase a saved game file, highlight the file you wish to delete and hold Select, press A + B.
EX Puzzle Mode
Once you beat the puzzles in the Ultra puzzle mode you will see what looks like a final puzzle. When you select this final item you are taken to the game's title screen. Now you can select any of the 12 EX puzzles that border the screen.
EX Puzzle Mode (Wario)
After you beat all 13 (be sure to play the puzzle in the middle of the screen) of Mario's EX Mode Puzzles, this mode opens up.
Ultra Puzzle Mode
Beat Wario's Special puzzles to unlock the Ultra puzzle difficulty. (It is not yet clear whether or not you need to beat Mario's Special puzzles first as well to unlock this new mode.)