What are the important gifts and graces given to Mary to become Mother of the Church?

Mary is universally acknowledged by the Catholic Church as the Mother of the Church, and this year our beloved Pope Francis officially declared the title a Feast having calendar it's commemoration the next day (Monday) week after Pentecost Celebration.

Source: Mary, Mother of the Church: A New Celebration

Catechism of the Catholic Church

Paragraph 6. Mary - Mother of Christ, Mother of the Church

963 Since the Virgin Mary's role in the mystery of Christ and the Spirit has been treated, it is fitting now to consider her place in the mystery of the Church. "The Virgin Mary . . . is acknowledged and honored as being truly the Mother of God and of the redeemer. . . . She is 'clearly the mother of the members of Christ' . . . since she has by her charity joined in bringing about the birth of believers in the Church, who are members of its head."⁵⁰² "Mary, Mother of Christ, Mother of the Church."⁵⁰³

⁵⁰² LG 53; cf. St. Augustine, De virg. 6:PL 40,399.
⁵⁰³ Paul VI, Discourse, November 21, 1964.

. . . she is our Mother in the order of grace

967 By her complete adherence to the Father's will, to his Son's redemptive >work, and to every prompting of the Holy Spirit, the Virgin Mary is the >Church's model of faith and charity. Thus she is a "preeminent and . . . wholly unique member of the Church"; indeed, she is the "exemplary realization" (typus) of the Church.*

968 Her role in relation to the Church and to all humanity goes still further. "In a wholly singular way she cooperated by her obedience, faith, hope, and burning charity in the Savior's work of restoring supernatural life to souls. For this reason she is a mother to us in the order of grace." ⁵¹¹

969 "This motherhood of Mary in the order of grace continues uninterruptedly from the consent which she loyally gave at the Annunciation and which she sustained without wavering beneath the cross, until the eternal fulfillment of all the elect. Taken up to heaven she did not lay aside this saving office but by her manifold intercession continues to bring us the gifts of eternal salvation . . . . Therefore the Blessed Virgin is invoked in the Church under the titles of Advocate, Helper, Benefactress, and Mediatrix.⁵¹²

The above article of faith & teaching comes from the Catechism of the Catholic Church.

Biblical basis

To answer biblically some important passages why Mary is the Mother of the Church Genesis 3:15 provides the starting point. Mary is the Mother of Christ, and Jesus is the 'HEAD OF THE CHURCH". Jesus was born in the most pure womb of Mary.

The Church, the Mystical Body of Christ is born thru Mary's too, How? Biblically speaking Catholic Church always point to John 19:27 and the Pentecost experienced at the Upper Room.

But since Genesis 3:15 passages point to Mary as the Mother of the Savior. The succeeding verse gives us the reflections how can Mary become our Mother right after the Fall of Adam & Eve.Genesis 3:16

"To the woman also he said: I will multiply thy sorrows, and thy conceptions: in sorrow shalt thou bring forth children, and thou shalt be under thy husband's power, and he shall have dominion over thee." (Genesis 3:16)

Now let's look at the word "IN SORROW SHALT THOU BRING FORTH CHILDREN"

Mary by Her fullness of grace, knows the Mission of Christ in the Redemption of Mankind, and in Her "sea of bitter sorrows" experienced in Calvary. Mary united the sufferings of Her Immaculate Heart to the Heart of Jesus in redeeming all sinners.

That's why AT THE FOOT OF THE CROSS, the agonizing Jesus seeing that Mary accepted all the redeemed in Her Immaculate Heart said the words "Woman, behold your son". Jesus knew Mary wants to follow further the Will of God not just in Redeeming the sinners but all the way to the Salvation of Souls.

While God prepared a body and preserve the sanctity of Mary's womb a fitting vessel or tabernacle for the Logos/Incarnate.

Mary's Immaculate Heart by Her perfect offering of her Seven Sorrows, Her Immaculate Heart becomes the fitting vessel for the Holy Spirit to dwells fully.

So, in the words of St. Louis De Montfort if the HEAD of the Church comes from the body of the Blessed Virgin Mary the Church the Mystical Body of Christ must come from the same body too.

St. Louis De Montfort states

" all the elect are in the womb of Mary".

Jesus the Head of the Church was bore in the most pure womb of Mary and all the redeemed was bore by Mary's perfect sorrows in Her Immaculate Heart.

To the question can Mary hear all the prayers of all the Redeemed numbering billions for Catholic alone, the answer can be found in Wisdom 1:7. Mary merited in Her Sorrowful & Immaculate Heart the fullness of the Holy Spirit dwelling more than Overshadowing. The Sevenfold gifts of the Holy Spirit empower Mary to hear every utterances of every soul; Wisdom 1:7 New American Bible (Revised Edition) (NABRE):

"For the spirit of the Lord fills the world, is all-embracing, and knows whatever is said."

Mary having a "glorified body" as envisioned by St. James the Greater in the year 40AD which is called the "Pre-Assumption Apparitions", and the Sevenfold gifts of the Holy Spirit this two Great Gifts enables Mary the Mother of the Church to transcends space & time and hear all the utterances of all believers in the power of the Holy Spirit.

These gifts, graces and unique role of the Blessed Virgin Mary is the pending 5th Dogma of the Catholic Church:

Mary is the Co-Redemptrix, Mediatrix of all graces and Advocate.