Very interesting and thought provoking questions. but I do have to say, those appear to be loaded questions
I do believe God reveals Himself to us through anthropomorphic revelation. He does not have eyes, yet, Scripture says He does. It's like when Jesus was talking to Nicodemus about rebirth. He asked him how He could tell him spiritual things if he didn't even understand earthly things. If God revealed even the slightest heavenly truths, we probably wouldn't understand it. But that is part of the glory of God. For all eternity, He will be revealing Himself to us!
I agree with your logic. If you run the thought of God having to learn something from His creation, well, I shudder at even the thought of it. It does not coincide with what the overall picture Scripture presents.
But therein lies the paradox. How can our prayers effect God if,
A. He knows all things - 1 John 3:20 and
B. If He works all things together according to His will - Ephesians 1:11.
But, there it is, out comes James 5:16, which says,
"Therefore, confess your sins to one another, and pray for one another, so that you may be healed. The effective prayer of a righteous man can accomplish much."
I'll be honest, I struggle over what the sovereignty of God means. You have a lot of Scripture for both sides of the issue.
Some regard it as God micromanaging every single act, no matter how minute, and saying that free will does not truly exist.
Then you have the other camp which is just the opposite extreme.
One camp says God peeks through time, therefore He knows all, and the other says He knows all because He does all, and doesn't have to peek.
I believe that He is outside of time, He is, and was, and is to come. That changes things as He would be seeing all of history as we see today, the here and now.
I kind of vacillate between the two thoughts because in the end, God can do whatever He jolly well wants to.
As for prayer, maybe it's not us changing God's mind, but Him changing ours? The closer we come to Him, the closer we are supposed to be conforming into the image of His Son. That would show that we are praying according to His will, therefore, He was just waiting on us to get it.
It's late, and I'm rambling. I may or may not of answered a single question, but I don't know if that's why you asked them in the first place. I say that, in part, because of your signature.