Sturdy works for both attack damage AND non-attack damage. So whenever a Sturdy character of yours would take damage from an opponent’s character or battle card, regardless of when or how, that would be reduced by 1.
No, a character that is Sturdy, cannot become or gain Sturdy again. The ability is binary; you either are Sturdy or are not, so a character can’t even have multiple instances of the ability.
Sturdy is applied anytime you would take damage in the game. Yes, you can reveal Survive on your turn if your character would take damage from an opponent’s character or battle card during your turn for any reason (for example: Rumble’s Revenge effect)
Sturdy works for both attack damage AND non-attack damage. So whenever a Sturdy character of yours would take damage from an opponent’s character or battle card, regardless of when or how, that would be reduced by 1.