The answer to the second question is spiritual. In the Old Testament, some crimes (sins) had the penalty of physical death and I have never seen anything to tell us that true repentance (which must include a change of heart) would exempt a person from that penalty. And in the end, we all die physically. (Heb 9:27 And as it is appointed unto men once to die, but after this the judgment:) In the spiritual, however, God delights in forgiving those who come to Him with a true heart of repentance and give them eternal life.
In reference to the first question, we are told in the Psalms:
Ps 103:10 He hath not dealt with us after our sins; nor rewarded us according to our iniquities.
11 For as the heaven is high above the earth, so great is his mercy toward them that fear him.
12 As far as the east is from the west, so far hath he removed our transgressions from us.
13 Like as a father pitieth his children, so the LORD pitieth them that fear him. (KJV)
We are told clearly that His mercy is for those who “fear” Him. That is, for those who hold God in great reverence, awe, and a positive fear. In Ezekiel 18: 21-22, the wicked man that turns from his sin is just what God is looking for. He's the one that can be forgiven, taught, and led in the way of righteousness.
This is what grace is all about. The forgiveness of a sin that is truly repented of and turned from. This is why God repeatedly pleads with us as in Ezekiel 18:30-32.
Eze 18:30 ¶ Therefore I will judge you, O house of Israel, every one according to his ways, saith the Lord GOD. Repent, and turn yourselves from all your transgressions; so iniquity shall not be your ruin.
31 Cast away from you all your transgressions, whereby ye have transgressed; and make you a new heart and a new spirit: for why will ye die, O house of Israel?
32 For I have no pleasure in the death of him that dieth, saith the Lord GOD: wherefore turn yourselves, and live ye.
Let's look at this grace in the New Testament beginning in Romans chapter 5.
Ro 5:12 Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned:
19 For as by one man's disobedience many were made sinners, so by the obedience of one shall many be made righteous.
20 Moreover the law entered, that the offence might abound. But where sin abounded, grace did much more abound:
21 That as sin hath reigned unto death, even so might grace reign through righteousness unto eternal life by Jesus Christ our Lord.
First, it is important that we recognize that we are condemned to both physical and spiritual death because we have sinned, not because Adam sinned. It is a result of Adam's sin but we are responsible for our own sin.
Next, we see in verse 21 that sin has reigned unto death but Jesus brought grace that we might gain eternal life. Here's how it works; just as sin has reigned in us unto death, even so might grace reign through righteousness … unto … eternal life … by Jesus Christ our Lord.
Chapter 6 gets into the details.
Ro 6:1 ¶ What shall we say then? Shall we continue in sin, that grace may abound?
2 God forbid. How shall we, that are dead to sin, live any longer therein?
Verse 1 poses a rhetorical question: Shall we continue in sin … ? NO WAY! Then comes another interesting question: How shall we that are dead to sin … ? Dead to sin? Not any longer live therein??? Fortunately, the rest of the chapter digs into what that means and how we live that way.
Ro 6:4 Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life.
5 For if we have been planted together in the likeness of his death, we shall be also in the likeness of his resurrection:
6 Knowing this, that our old man is crucified with him, that the body of sin might be destroyed, that henceforth we should not serve sin.
7 For he that is dead is freed from sin.
Now, I realize that many might have trouble with concept of “newness of life”, “henceforth we should not serve sin”, and “he that is dead is freed from sin”. You might be tempted like many others to say, Sure, when you're dead and gone, sin has no hold on you! Remember verse 4 and verse 6 … we are buried with him, our “old man” is crucified, we are a new creation.
Ro 6:11 Likewise reckon ye also yourselves to be dead indeed unto sin, but alive unto God through Jesus Christ our Lord.
12 Let not sin therefore reign in your mortal body, that ye should obey it in the lusts thereof.
13 Neither yield ye your members as instruments of unrighteousness unto sin: but yield yourselves unto God, as those that are alive from the dead, and your members as instruments of righteousness unto God.
14 For sin shall not have dominion over you: for ye are not under the law, but under grace.
Remember chapter 5, verse 21? … “even so might grace reign through righteousness … unto … eternal life … by Jesus Christ our Lord.”
2Co 5:17 Therefore if any man be in Christ, he is a new creature: old things are passed away; behold, all things are become new.
18 And all things are of God, who hath reconciled us to himself by Jesus Christ, and hath given to us the ministry of reconciliation;
Ga 2:20 I am crucified with Christ: nevertheless I live; yet not I, but Christ liveth in me: and the life which I now live in the flesh I live by the faith of the Son of God, who loved me, and gave himself for me.
Ga 5:16 This I say then, Walk in the Spirit, and ye shall not fulfil the lust of the flesh.
Ga 6:14 But God forbid that I should glory, save in the cross of our Lord Jesus Christ, by whom the world is crucified unto me, and I unto the world.
15 For in Christ Jesus neither circumcision availeth any thing, nor uncircumcision, but a new creature.
1Jo 2:6 He that saith he abideth in him ought himself also so to walk, even as he walked.
I highly recommend reading Romans 6 slowly, carefully, and thoughtfully. Then chapter 7 the same way. When you get to verse 14, stop and read chapter 6 again with chapter 7 verses 1-13. Think about verse 9 and then consider 1 Cor. 13:11. From there go back to Romans 7 verse 14 and read through chapter 8 verse 16. Ezekiel 18 makes much more sense when we see the heart of God to love and forgive those who will heed His call.