The controller (not the owner) of "Guardian Angel Joan" increases his/her Life Points.
When "Guardian Angel Joan" is destroyed while battling a monster with equal ATK (such as another "Guardian Angel Joan"), her effect is NOT activated because "Guardian Angel Joan" has been removed from the field.
When "Guardian Angel Joan" attacks "Cyber Jar", "Guardian Angel Joan"'s effect is not activated because she is destroyed before "Cyber Jar" is sent to the Graveyard.