Then God said, “Let us make mankind in our image, in our likeness, so that they may rule over the fish in the sea and the birds in the sky, over the livestock and all the wild animals, and over all the creatures that move along the ground.” So God created mankind in his own image, in the image of God he created them; male and female he created them.
That appeals to man's vanity. The problem with vanity is envy soon follows, which is the motivation behind most of the evil in the world. Most evil can be traced back to the sin of pride, and the image of God idea is the ultimate pride. It is highly doubtful the image of God is anything resembling man.
This is a typological reference to the Trinity
No, you are in error because you do not know the Scriptures or the power of God. (Matthew 22:29). God made man to rule over the earth. The first sin came when Eve was deceived into thinking "you will be like God" (Gen 3:5) Eve sinned because she did not know the command (singlar!) of God. She added to the command God had given, making it seem unreasonable, as God prohibitted only eating of the fruit, and she added touching as well. (Gen 2:17, Gen 3:3)
You are correct in saying that we are far removed from God, especially since he "...alone is immortal, and lives in unapproachable light, whom no one has seen or can see." (1 Timothy 6:16). God is spirit (John 6:24) and invisible (1 Timothy 1:17).
However, we learn from the NT that Jesus is the image, the manifestation, the very essence of God in bodily form (Colossians 1:15, Phillipians 2:6-7). In fact, Jesus Christ created all things! (Colossians 1:16, John 1:3, 1:10). We also find that Jesus existed before creation (obviously, if the previous were true), and was planned to die sacrificially before the creation of the world! (1 Peter 1:20, Rev 13:8).
Since God walked in garden in the cool of the day (Genesis 3:8), he must have had bodily form. Thus, it is logical to conclude that God manifested himself in Jesus to interact with Adam. Since Jesus was the man-God, we are made in his image, not the other way around. Bodily, emotionally, sensorily, and with a free will.