Mary is the first person who knows and believes in Christ.She is the first Christian and so all our spiritual mother.I think it is appropriate.
However , the title of Mother of ALL people and ALL Living seems incorrect. Because all people/All living also include those who do not believe in Christ. And this also means that Mary is the mother of those who are not in Christ,e.g. non-christians.
It's my understanding the The Theotokos is called the "Mother of the All the Living" because she is the Second Eve, as Christ is the Second Adam. Where Eve is tempted and disobeys, the Blessed Virgin is obedient and bears the savior of the world.
She becomes the Mother of All the Living by virtue of her fulfilling the role that Eve was given in the beginning, to be submitted completely to the will of God just as Christ is submitted to the will of God even onto death, and death on a cross.