Here is the question:
"Here's a paradox that actually comes from Christian teaching: To be human is to be imperfect and have limited knowledge. So how could an omnipotent God experience what it is like to be human? How could Jesus actually suffer like us when he knows that he is God?"
I would say that the alleged paradox confuses categories. You are confusing human perfection with divine omnipotence by assuming that perfection means qualities of infinitude; but in humans, imperfection means moral imperfection. Now, God's attributes are typically divided into communicable ones and incommunicable ones. His communicable attributes are the ones he instills in humans at the creation: goodness, righteousness, love, beauty. But his incommunicable attributes are the ones he has within himself, and does not share with humans i.e., omniscience, omnipotence, omnipresence, et. al., and these are subsumed in a perfect coalescence--including his moral purity, justice, love, holiness, and love (too name some, but not all). Further, God's perfection is thus different than human perfection is, and therefore to be a perfect human does not mean that the human needs to have an infinite coalescence of divine, incommunicable attributes. Adam was perfect at his creation, and this means he was without sin, but he was also finite. No problem.
Now it's true that humans have limited knowledge, as God has infinite knowledge (we may even grant that such knowledge is "perfect," as in exhaustive, but God's knowledge is both actual in infinitude and realized in time), and for God to become a man would indeed limit both his knowledge and his power (Jesus grew in stature and wisdom as a child).
The proper question would be, "To be human is to be finite, and have limited knowledge, so how could an infinite God experience what it is like to be human?" The councils of Nicea and Chalcedon tried to hash these things out: just who was Jesus of Nazareth? The conclusion drawn from Scripture and reason was that Jesus was (is) one person with two natures (God-nature, and man-nature). Theologians describe what happened: God, in Jesus, limited himself in his incommunicable attributes of omnipresence, omnipotence, etc. His communicable attributes of love, goodness, holiness, etc. were not limited. How can this be? How did he do it? There are such things as mystery in our religion....
But the paradox mentioned is real: in his almighty power, he limited himself in that power. But paradoxes are not contradictions; we may grant that paradoxes are related to "mystery," and with this I am happy to affirm as true. But a contradiction, according to Aristotle, is that
- "it is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect."
Jesus, in his person, belongs to both his divine nature and his human nature, but we don't say that Jesus' human nature belonged and did not belong to his person; nor do we say that his divine nature both belonged and did not belong to his person. For both natures to belong to one person is not a contradiction, but for God to become a man is most certainly a paradox. And with this we can live.
A classic christological text is Philippians 2:5-10 and can be read here.