I'll respectfully disagree on this issue. God asks us to "reason" with Him (Isaiah 1:18). While we certainly do not match His intellect (Isaiah 55:9), He certainly does not ask us to accept irrational or illogical positions.
Jesus said, "I am the way, the truth and the life," (John 14:6). If He is Truth, then he cannot lie, logic is truth, and therefore God cannot be illogical.
Let me take a stab at your conundrums:
Why did God simply decide to punish Satan in the Garden of Eden, why not just destroy him right then and there?
Man was originally created with the ability to not sin. The Tree of the knowledge of good and evil is a choice. The serpent is temptation toward a wrong choice. Once man freely chose disobedience, choosing sin over God, his eyes were opened to all manner of evil. Consider the shame of nakedness that was not shame just prior to his wrong choice.
The only thing that changed when man chose sin is that his eyes were open to see evil, and be unable to refrain from it. Hence another way of saying that "sin entered the world" is to say that "innoncence left man".
God desires that man choose freely to love Him. That's why He gave us free will. Had he destroyed man or the serpent after the fall the free will creature that He created for fellowship would no longer exist. The Good News is that He was fully aware of this, and instituted a plan to save man from his own bad choice, even before He created him.
Why did Jesus have to come and be crucified for our sins? Couldn't God have simply forgiven them?
No. God has said that sin = death. If you sin, you will die (Genesis 2:17). The entire OT sacrificial system was instituted to offer substitutonal deaths on account of man's sin. However, it took a Perfect Sacrifice of The Infinite Being to pay for the sin of all men.
Think about God as the perfect Accountant. His books must be in order. Every man who sins owes a death. The man, Jesus, did not sin therefore he does not owe a death. Yet He died. If Jesus is merely man, then one man who sinned would be able to escape death - God is perfect, so He must keep the books balanced.
However, Jesus was not merely man. He is is also God. Therefore, as man he kept God's ordinance perfectly. As God, and serving as the Perfect sacrifice on the cross, an infinite being suffered the punishment which was undeserved. Hence, the fact that Jesus is God, therefore infinite, His sacrifice is perfect and complete for all men. The payment of the Infinite One can be fully applied to anyone who believes and obeys Him!
Why did God seem to give us things "piecemeal"?
This is the easy one. It is answered very clearly by Paul in 1 Corinthians 2:
7 But we speak the wisdom of God in a mystery, the hidden wisdom which God ordained before the ages for our glory, 8 which none of the rulers of this age knew; for had they known, they would not have crucified the Lord of glory.
The bottom line is that if anyone or any church asks us to accept a tenet blindly, or accept anything irrational, illogical, contradictory, their teaching must be in error. God is Truth, and cannot lie- Even He cannot make 1 + 1 equal 3.
"No. God has said that sin = death. If you sin, you will die"
So, if you never sin, you will never die?