Explanation: Nationality is a permanent identity, so we use SER. "Ella es mexicana" = She is Mexican.
Explanation: Location requires ESTAR. "El libro está en la mesa" = The book is on the table.
Explanation: Profession is a permanent identity, so we use SER. "Yo soy profesor" = I am a teacher.
Explanation: Asking about someone's condition/state uses ESTAR. "¿Cómo estás?" = How are you?
Explanation: Origin (where you are FROM) is permanent and uses SER. ESTAR is only for temporary location (where you ARE NOW).
Explanation: A current condition or state uses ESTAR. The door is IN A CLOSED STATE now, so "está cerrada".
Explanation: A personality trait or characteristic is permanent, so we use SER. "Mi padre es inteligente" = My father is intelligent.
Explanation: Current location uses ESTAR. "Yo estoy en Barcelona" = I am in Barcelona (right now, but I might leave).