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>God in the OT had a much more "violent" or "volatile" demeanor compared to the NT,
Pedant's corner: God in the OT seems more like that because not only does it cover millenia, so it has more ground to cover, but also (mainly) because man kept fouling up so badly that it incited Him to anger and to punish us.
>in Scripture has God ever been characterized as all-loving or omnibenevolent?
Yes. There are countless references to His love and goodness in the Psalms alone.
>Interestingly - and pardon me for the example - but the Qur'an doesn't seem to describe God completely as omnibenevolent, and in the 99 Names of Allah the Islamic God is characterized with attributes as a Destroyer in a much more impersonal manner than the one we get to know with Christianity, making him an ambivalent God in which everything is already determined (In'shallah, aka, God willing…implying determinism?) and having more realistic attributes that are in par with what we know of how the world operates, in a volatile and not necessarily just manner.
But the Qur'an is trash. That it doesn't describe the Lord as loving is proof of this.
>It seems that both Gods do what they please, and are willing to intercede in prayer, but is omnibenevolence ever mentioned in the Bible, or is that just a popular belief given the loving attributes of Jesus Christ?
Yes, it is referenced all throughout scripture. The very fact that we have scripture is evidence of His love and benevolence for us. If Christ is the Son, and the Son shares the same nature as the Father, then it follows that the Father too is love and goodness.
Prayer is also about praising, begging forgiveness, and seeking to unite oneself more closely to His will, since He is the highest good.
>Does God cause good and evil for reasons we don't know?
God is not the author of evil. He permits it that good may come of it. The greatest evil, and simultaneously the greatest good, is the Crucifixtion. That's all we need to know.
>Could this be an argument for believing that the Father, the Son, and the Holy Spirit are three different divine entities, making the Father ambivalent and the Son benevolent, as he atoned for our sins?
No, Marcion, is does not. The Son was sent at the command of the Father, and makes explicit references in the Gospel to doing the Will of the Father. If Christ, being perfectly obedient, atoned for our sins, then it follows again that this was His charge from the Father. If Christ atoned for our sins, but the Father was only ambivalent about it, then it likewise follows that Christ wasn't doing the will of the Father.
>I need a sound argument against the Problem of Evil and injustice and how would Jesus allow such things to happen and be powerless against preventing them despite being omnipotent.
<Where is the wise? Where is the scribe? Where is the disputer of this world? Hath not God made foolish the wisdom of this world? For seeing that in the wisdom of God the world, by wisdom, knew not God, it pleased God, by the foolishness of our preaching, to save them that believe. For both the Jews require signs, and the Greeks seek after wisdom: But we preach Christ crucified, unto the Jews indeed a stumblingblock, and unto the Gentiles foolishness: But unto them that are called, both Jews and Greeks, Christ the power of God, and the wisdom of God. For the foolishness of God is wiser than men; and the weakness of God is stronger than men. For see your vocation, brethren, that there are not many wise according to the flesh, not many mighty, not many noble: But the foolish things of the world hath God chosen, that he may confound the wise; and the weak things of the world hath God chosen, that he may confound the strong. And the base things of the world, and the things that are contemptible, hath God chosen, and things that are not, that he might bring to nought things that are: That no flesh should glory in his sight. But of him are you in Christ Jesus, who of God is made unto us wisdom, and justice, and sanctification, and redemption: That, as it is written: He that glorieth, may glory in the Lord. (1 Cor 1:20-31)
God bless you! He is risen!