I think the foundational questions are:
1. What is sin?
answer - acting contrary to the will of God.
2. What is truth?
answer - what God defines it to be. If there is no all-powerful, all-knowing God there is no absolute truth.
God acts according to His sovereign will. He alone has the ultimate form of free will. He also cannot sin because doing so would be acting against His own will.
The truth is defined by God. Therefore He cannot lie.
Actually, that is not a bad definition. It is not only biblical, it is logically. Think about it for a moment. No orthodox Christian will say that God can sin. We know the ramifications if God ever sins. Why cannot God sin? The Bible says that God is holy. Holiness is inherent to His nature. Ergo, God cannot sin because His holy nature will not allow it. That is not a Monergist statement, it is simply an unassailable fact.
God does not possess a free will in the way that we interpret the term. When we think of free will we usually juxtapose a decision we need to make against all available alternatives and make the decision that we believe is in our best interest. God does not need to do that. Eph. 1:11 says He works all things after the counsel of His own will. God does not need to consider all available options. God's will is perfect. He just acts according to His predetermined plan.
If God does not have free will no one does and free will is a fantasy.
This is the end product of the theologies of man.
Isaiah 55
8 For my thoughts are not your thoughts, neither are your ways my ways, saith the LORD.
9 For as the heavens are higher than the earth, so are my ways higher than your ways, and my thoughts than your thoughts.
I'm just going to be frank. It's a stupid question. Does God have free will?
What does that even mean. GOD IS GOD and you are not. HE does whatever He pleases. Stop putting Him under a microscope. Bow your knee to Him and Worship Him and He will privilege you with revelation of Himself. (I'm using "you" generally)
Once again, please explain why millions of unregenerate people baptize their infants, attend church, pray, take communion, etc. if they do not desire to please God. I'm not saying they are pleasing God, I am saying they desire to please God. Why aren't these people desiring to please God?