It's not "new" life; it's the same life, but changed. It's not a new heart, but a changed heart. It's not new will, but changed will.
You die to your old ways and are "born again" in new ways. It's like being a habitual smoker and kicking the habit with God's help.
If you are truly a reformed smoker or a reformed alcoholic, you will never go back to either.
The penalty of sin is death
Yes because unrepentant sin is separation from God, who is life. He is our life-support System.
The blood of the Lamb covered the sins of many, giving new life to those who believe on Christ.
That is not the uninterrupted teaching of the Church. Christ took the sins of all mankind on himself as ransom for our freedom from death. That was a gift.
With the freedom He gained for us, those who come to Him freely in Baptism and Faith are justified in God's eyes. That we have to work for by dying to our old ways and living a life of imitating Christ.
The Bibles teaching about unregenerate man is not contained in those 3 verse you cited
So what makes Paul greater authority than Matthew, Mark or Luke? The teaching about the unregenerate man is Paul's theology, not the teaching of the Bible as a whole, or for that matter the Church as a whole.
You expressed that beautifully,Dear Brother.May God Bless you