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.
In a Two-Headed Giant game, your life total is your team's life total.
If your life total is negative, X is considered to be 0. (This is a change from previous rulings.)
Standard: Ej legal
Pioneer: Ej legal
EDH / Commander: Restricted
Pauper: Ej legal
Brawl: Ej legal
Historic: Ej legal
Premodern: Ej legal
93/94: Ej legal