HP: Belief is not all that is needed to be saved. One must first repent.
As for baptism washing away original sin, where is the slightest evidence of that?? Certainly the passages you mentioned do not establish any such notion.
Isaiah 43: 27; "Your first father sinned, and your mediators transgressed against me. "
Gen. 2:17 - the day you eat of that tree, you shall die. Adam and Eve ate of the tree, and they spiritually died. Some Protestant communities ignore or deny the reality of original sin. But if there is no original sin, then we do not need a Savior either. The horrors of our world testify to the reality of original sin.
Gen. 3:14-19 - God's punishment for eating of the tree was cursing satan, increasing women's pain in childbirth, and condemning man to toil and labor for his whole life.
Job 14:1,4 - man that is born of woman is of few days and full of trouble. Who can bring a clean thing out of an unclean? All humans are afflicted with original sin, and this includes babies as well. This is why the Catholic Church has baptized babies for 2,000 years.
Psalm 51:5 - I was brought forth in iniquity, and in sin did my mother conceive me. We have inherited Adam's sin from the moment of our conception. This is why babies need baptism – to wash away the original sin inherited from Adam and Eve.
Rom. 5:12 - sin came into the world through one man, Adam, and death came through this sin. This sin affects all people, men and women, babies and adults. Through the merits of Jesus Christ, we have the sacrament of baptism to wash away the sin that came through Adam.
Rom. 5:14 - death reigned from Adam to Moses, born from Adam's original sin. This is a mystery we do not fully understand, but we must all acknowledge our propensity toward evil and our need of God.
Rom. 5:16 - the judgment following one single trespass brought condemnation for all. This means all have inherited the sin of Adam, and all must be washed clean of this sin in the waters of baptism.
Rom. 5:19 - by one man's disobedience many were made sinners. Original sin is passed on as part of the human condition, and only God in the flesh could atone for our sins by the eternal sacrifice of Himself. Through this sacrifice, God has re-opened the doors to heaven, and through baptism, we are once again made children of God.
1 Cor. 15:21 - for by one man came death. In Adam, all die. In Christ, the new Adam, all now may live.
Eph. 2:1-3 - we were all dead through sin and all lived in the passions of our flesh until Christ came to save us.