I simply read in my bible in John 1:22 that "He is the atoning sacrifice for our sins, and not only for ours but also for the sins of the whole world." Reading a little further on in 1 John 4:14, I see this, "And we have seen and testify that the Father has sent his Son to be the Savior of the world." In his gospel, John wrote in the first chapter verse 29, "The next day he saw Jesus coming toward him, and said, “Behold, the Lamb of God, who takes away the sin of the world!" Therefore I believe what is written.
He
is taking away the sin of the world. See post above. That does not mean every individual. If it did, universalism would be true and no one would be lost. There is an active thread, Partial LA, in the Calvinism @ Arminianism board that deals with that scripture and this subject that you might find interesting. There are other views on the 1 John 4:2 scripture. And the one I give above is not my only reasoning.
Christ's sacrifice was infinite as He is and it provided grace enough for every living soul to be saved.
It could have but it was not intended to and it didn't. All through Scripture we see the atonement being for specific people. The "called" (start noticing all the places that is used within the writing of the apostles, often in the greeting portion. We tend to slip right over it.) "the elect","the chosen", "His sheep" "those God gives Him", "adopted." It is specific.
If we use the Old Testament to define God we will run into several contradictions about his nature.
They are not contradictions. If they are, then God is contradictory within Himself. Even though God is love, that does not mean that He loves sin or evil. Even though He is compassionate and full of loving kindness, that does mean He will not uphold His own law that says if you sin you die. Even though He is merciful He has common mercy and kindness to creation, bringing rain to the righteous and the wicked. His common mercy is what keeps the universe running faithfully, providing food for man and animal alike etc. He has a personal mercy, love, faithfulness, kindness, patience etc. for His covenant people. A love and mercy that gives them to Christ, and saves them from facing His wrath. When the Bible says He shows no favoritism, it is referring to the Jew and Gentile division. Both are saved and in the same way. It does not mean that He treats all people equally. All the unbelieving will face His wrath, and justly so.
Things such as His repentance, His anger, and His need to come down to see the city that men had built so we can't use the OT to prove one point while dismissing what the rest of it has to say about the nature of God.
Well those things are not about the nature of God. And if they were then He had no business for example telling us what He tells Job in the last chapters of the book. Or what He tells us is the Prophets about Himself. And if that is true, we might as well toss the whole book aside as we could never know when He might change His mind. Those places that you mention are the limitations of human language conveying what is unseen by what happens that we can see. It is what it looks like to us.