She died of natural causes on October 4, 1582.
St. Teresa was a nun of the Carmelite order and they survived primarily on donations and from articles they produced or grew at the convent.
No. She never married nor had any children.
Yes, Teresa was from Avila, Castile, Spain.
No, she was not a martyr. She died at the age of 67 from complications relating to the malaria she had contracted as a child.