However, Eve managed to sin quite willingly. If Eve is the model of Mary, then one can reasonably conclude that because Eve was not only capable of sin and did sin, so Mary was capable of sin and did sin.
If she never sinned she assuredly had no reason for the grace of God in salvation from sin and its effects.
No these are two quite different women.
Eve listened to the bad angel and contributed to the fall of man
Mary listened to the good angel and contributed to the salvation of man
Adam calls Eve 'woman'
Jeus calls Mary 'woman'
Eve prompted Adam to his first evil act
Mary prompted Jesus to his first glorious act at the Wedding in Cana
Eve was cursed for disbelief
Mary was blessed for she believed
Through Eve comes sin and death
Through Mary comes life and grace
Eve is the mother of all the living
Mary is the mother of all those who obey God and hold testimony to Jesus
By the grace of God Mary was born without 'original sin'. Catholics believe all man is born with original sin thanks to Eve.
Mary is the Ark of the New Covenant.
The Ark of the Old Covenant contained the Rod of Aaron, the High Priest.
The Ark of the New Covenant contained Jesus, the Eternal High Priest.
The Ark of the Old Covenant contained Manna, Bread for Earthly life.
The Ark of the New Covenant contained Jesus, Bread of Eternal life.
The Ark of the Old Covenant contained the 10 Commandments etched in stone - The word of God (small w)
The Ark of the New Covenant contained Jesus, the Word of God (capital W) the word of God made flesh