Today's Sudoku is one puzzle per day, generated from the date, so everyone who plays on the same calendar date gets the same grid. It changes at midnight on your device's clock. Each level has its own daily puzzle: switch levels with the menu above the board.
At midnight on your device's clock. It follows your device's date, so it changes with your local time zone.
Yes. You can replay the same puzzle as often as you like, and your best time is kept on this device.
By solving Today's Sudoku on consecutive days. Pressing Show solution does not count as a solve.