Invulnerability
Enter this code at the pause menu to toggle invulnerability on/off: L1, L1, L2, L2, R1, R1, R2, R2.

Unlock All Levels
Play the game until you have passed the first subway level. Once the next level has loaded, go to the main menu and press... UP, DOWN, LEFT, RIGHT, UP, LEFT, DOWN, CIRCLE. Go to the load menu and all levels should be unlocked. When you start each of the levels you will have the same inventory that you had when you completed the first subway level.

Unlock All Weapons
To unlock all weapons, enter this code at the pause menu: L1, L2, R1, R2, TRIANGLE, CIRCLE, X, SQUARE.