Bible passages are always helpful to support your case (as well as reasonable answers to reasonable questions). Yes God is love. He's also just. He loves righteousness and hates wickedness. Sorry but it's true.
Keep in mind the original question was about God loving forever (or not) those who are wicked and are eventually punished and cast into the depths of Hell:
Psalm 103:11, 17-18 For as the heavens are high above the earth, so his loyal love prevails over those who fear him.
But the loyal love of Yahweh is from everlasting to everlasting on those who fear him, and his righteousness to their children’s children, to those who keep his covenant and remember to do his precepts.
David's secure in God's love (Psalm 139). But what about the wicked that are cast into the depths of Hell??? Is God's Love present??? I think not:
1. Psalm 11:5 Yahweh tests the righteous, but the wicked and the lover of violence his soul hates.
2. Psalm 37:12-13, 28 The wicked plans evil against the righteous, and gnashes at him with his teeth. The Lord laughs at him, for he sees that his day is coming. For Yahweh loves justice and will not forsake his faithful ones. They are protected forever. But the children of the wicked will be cut off.
3. Psalm 97:10a You who love Yahweh, hate evil.
4. 2 Thessalonians 1:9 who will pay the penalty of eternal destruction, away from the presence of the Lord and from the glory of his strength,
I don't know why I'm answering your questions when you are not answering mine but here goes:
Yes, I believe God is omnipresent.
It's His creation. He can (and will eventually) punish what He hates by destruction. And sorry but the wicked most certainly pay the penalty of eternal destruction "
away from the presence of the Lord". If you think about it, it actually proves His righteous judgment.
2 Thessalonians 1:5-10 a proof of the righteous judgment of God, so that you may be considered worthy of the kingdom of God, on behalf of which also you are suffering, since it is righteous in the sight of God to pay back those who are afflicting you with affliction, and to you who are being afflicted, rest with us at the revelation of the Lord Jesus from heaven with his powerful angels, with burning flame giving punishment to those who do not know God and who do not obey the gospel of our Lord Jesus, who will pay the penalty of eternal destruction, away from the presence of the Lord and from the glory of his strength, whenever he should come to be glorified on that day by his saints and to be marveled at by all who believe, because our testimony was believed among you,