Death's Shadow's ability applies only while Death's Shadow is on the battlefield. In all other zones, its power and toughness are 13.

The value of X changes as you gain and lose life. It's not locked in as Death's Shadow enters the battlefield.

If your life total is 13 or greater and nothing else is boosting the toughness of Death's Shadow, it's put into its owner's graveyard as a state-based action.

If your life total is less than 0 and an effect (such as the one from an opponent's Abyssal Persecutor) is keeping you from losing the game, Death's Shadow's ability will actually increase its power and toughness. For example, if your life total is -2, Death's Shadow gets +2/+2.

In a Two-Headed Giant game, your life total is your team's life total.