> Since God is omnipresent (implying we're in God's presence) and Christians share a loving relationship with God, would you say Christians are in Heaven right now despite living on Earth?
God's presence, despite his omnipresence, seems to be something that is variable and manifests itself in different states and intensities. God is present everything, according to the theology of omnipresence, but after Solomon finished the temple the text says that God's presence descended on it. Obviously he was present in a different sense in the temple than his general omnipresence. And it seems he was present in an even different sense in the Holy of Holies, and then again in an even different sense on the bema seat of the ark of the covenant.
When Adam and Eve sinned (Genesis 3), their supreme loss was not access to the Garden of Eden, but access to God's presence. Obviously God's presence is variable and mitigated by many things.
Jesus was "God with us." Again, his presence in a different way and obviously a different reality and intensity.
Given those observations about God's presence, I would not say that Christians are in heaven right now despite living on Earth. Our relationship with God is real and vital, but 1 Corinthians 13.12 and 1 Jn. 3.2 let us know that what we are experiencing now is a partial picture of the full reality that comes later when we are actually in God's presence, so-to-speak "face to face."
> Also, if Heaven isn't a place but a relationship, then how would you explain why Matthew frequently alludes to the "kingdom" of Heaven?
The kingdom of heaven is generally interpreted to be "the reign of God." In a sense, the kingdom is where the king is. Theologically it is often spoken of as "already and not yet." We experience the kingdom of heaven on the earth since Jesus is in us, but there is a much fuller reality to come.
> What about Matthew 7:21, 12:50, 18:10, 18:14, or 23:9 which all state God the Father is in Heaven?
If "heaven" is "the presence of God," the Father can be nothing but.
> Isaiah 66:1; Acts 7.49; Ps. 103.19
The ancients perceived heaven as a location. They viewed the "firmament" (Earth's atmosphere) as a solid dome above the earth, with God's throne situated on the external apex.
> Rev. 21
In this case "heaven" is "the sky": Earth's atmosphere and outer space. Revelation is rife with phenomena of cosmic breakdown: stars falling from the sky, moon turning to blood. Here "the heaven" refers not to the dwelling place of God but to "the heavens"—what we see when we look up. But it's all imagery. The verse also says "there was no longer any sea," which is an image of chaos.
> Jn. 14.2
The disciples, who were known to think concretely and who seemed to be quite dense about Jesus's spiritual meanings, are probably thinking He is referring to the Temple itself. They are in the vicinity of Jerusalem. Being familiar with they prophecies, they were still expecting a grand Messianic arrival. When Jesus speaks of many rooms in the Father's house, they are likely thinking of the Jerusalem Temple, the Lord suddenly coming to His temple (Mal. 3.1-4), and quarters for them to live with His there and share in His reign.
In truth, since Jesus always speaks in layers of meaning, Jesus is cryptically referring to His death the next day, their joining Him in death via martyrdom, and their subsequent glorification with Him on the basis of His resurrection. The Temple is but a shadow of God’s presence.
> Jn. 3.13
What Jesus is talking about is the ability to understand such spiritual mysteries. Jesus is pre-existent and has been in the presence of God. He has direct knowledge of the mind and action of God. The term "heaven" here emphasizes Jesus's timeless existence and his first-hand knowledge of the things of God.