You said, "People, and sometimes nations, guilty of extreme or extended sin were killed, but this was not murder but avenging the wickedness caused by these people or nations." I agree with this statement, but it is hard to understand because, in the New Testament, we get this picture of God that is very, very gracious and understanding, but still to be revered. But it seems in the Old Testament, those who were wicked were condemned to death seemingly taking away their chance at repentance. For example, Sodom was destroyed for their perversion and corruption. Did God know that none of them would repent? Even the man on the cross who was being punished for his wickedness was able to repent. Obviously, as he is told, "today you will be with me in Paradise." Today, no matter what degree of wickedness a man has, he is given a chance to repent. Was it Dromer, the mass murderer, who was converted in prison before his execution? How do we reason with this, because we know that God wouldn't change?
Let's start with a fundamental concept and build up from there. The Bible is clear that the nature and character of God do not change. "God is not a man, that He should lie, nor a son of man, that He should repent. Has He said, and will He not do? Or has He spoken, and will He not make it good?" (Numbers 23:19). It does not mean God doesn't change His mind concerning man, such as in Genesis 6:5-6), but that is not because God changes but because man changes. Therefore, when we talk about the God of the Old Testament and the God of the New Testament, we are not talking about two different beings. He is one and the same; just as it is said about the Son of God, "Jesus Christ is the same yesterday, today, and forever" (Hebrews 13:8). God doesn't change. "Like a cloak You will fold them up, and they will be changed. But You are the same, and Your years will not fail" (Hebrews 1:12).
It is in the New Testament that we are warned, "Therefore consider the goodness and severity of God: on those who fell, severity; but toward you, goodness, if you continue in His goodness. Otherwise you also will be cut off" (Romans 11:22). What is happening is that you are oversimplifying your view of God. You are focusing on His love while ignoring His justice, but God is both.
How long were the people of Sodom involved in sin before God finally decided to destroy them? "And the LORD said, "Because the outcry against Sodom and Gomorrah is great, and because their sin is very grave, I will go down now and see whether they have done altogether according to the outcry against it that has come to Me; and if not, I will know" (Genesis 18:20-21). God wanted Abraham, and us as well, to know that the destruction of Sodom was not arbitrary or spur of the moment. He personally checked out the situation! He even agreed to not destroy the cities (there were five involved, though one was spared for Lot's sake) if He could find just ten righteous people in the area (Genesis 18:32). So why were the cities destroyed? Because of their grave sins and the fact that only four righteous people were found. There was an opportunity for more to leave than just four, but none would listen. So where was the lack of a chance to repent?
How many "one more chance" does a person need? I can't answer that question. No man could because we can't read the mind of a man. But God can. God allows this world to continue so people can have a chance to repent (II Peter 3:9), but it won't last forever. An end is planned (II Peter 3:10-12).
Ultimately, every man has a choice whether to choose sin or righteousness. This is the guaranteed choice that we all have (I Corinthians 10:13). No one has to sin. Everyone chooses to sin and the consequence of that sin is death (Romans 6:23). God is gracious and merciful toward us in that he doesn't give us what we have justly earned immediately. He has demonstrated great love toward us in that we don't have to earn our salvation back because none of us would be able to earn it. But what you are doing is turning it all around and saying, "Yeah, I know I earned death, but I want another chance ... maybe." If that endless one more chance isn't given you want to cry "UNFAIR!" "Yet the house of Israel says, 'The way of the Lord is not fair.' O house of Israel, is it not My ways which are fair, and your ways which are not fair?" (Ezekiel 18:29).
I wrote a study not too long ago about the nature of God. It will take a bit of time, but please go through The Lord Your God is an Awesome God! It will take you through the Scriptures and give you a better appreciation for the nature of the God you and I serve.