I want to first point out, that you did not answer any of the questions.
Can you really apply this law to God? Is God subject to any law?
You give it a try and let's see if you are successful. You apply a law to God.
You can attempt to dip and dive all you want. Although I'm curious what ground you are standing on when you ASSUME that God can't be understood through Logic. You are answering a question with a question. You are ASSUMING. Obviously, if there is a God (and there is) then we cannot fully comprehend such a being. However, we can apprehend. Particularly, if said God created human beings to do that very thing. And if God upholds the laws of nature, then He also upholds the laws of logic. That are an outflow of His being.
The question, 'is God subject to any law' presumes a source outside God, and you will certainly find that a dead end. In other words, if you ask the wrong question, you will always get the wrong answers. So as Byb has tried to explain, it is about the essence of God. His goodness, truth, etc.
It's like asking you to open your eyes and not see what's in front of you. Your vision, by its nature, will produce sight. You WILL see because you have sight. God's goodness, love, justice, truth etc., means He will
be according to such. If God is goodness then to say He is not goodness is a logical contradiction. When God described Himself to Moses He said, "I am." A statement that is consistent with God being pure being. God completely knows Himself.
The simple fact that you say that God can't change himself... Why wouldn't he be able to change himself?
The issue of changing is addressed by Aquinas and has to do with contingency, and also with actuality versus potentiality. If God has potential then He has traits that have yet to come into actuality. It is a difficult issue I admit, and one that will not be answered with one night flipping through Google. Nor will googling objections to divine simplicity and trying to build your case from others arguments you don't understand.
If you desire to study immutability, aseity, etc. then this is covered in detail. Probably more in-depth than we could offer up in a thread. Jac is our resident philospoher and he'd probably make the same recomendation to you that He did to me. For starters you can read his thesis on divine simplicity.
http://cmmorrison.files.wordpress.com/2 ... licity.pdf And Edward Feser's Beginners Guide to Aquinas. Most importantly Feser is a contemporary philospher who deals with a lot of the objections and miconceptions about divine similicity.
Now, will you answer the questions?