Unfortunately the laws of logic cease to exist if there are no minds form logical thoughts. Does the same thing apply to God? This would definitely destroy the idea that he is omnipresent and potentially all powerful.
There is no mathematical or scientific evidence for God or a god. Also it is not logical or reasonable to assume that God or a god exists. It is not logical or reasonable to assume anything. But as was previously stated, we have to assume that our thoughts are even related to reality. I don't think that is a very good argument because it is unable to be tested or proven. We have absolutely no reason to believe that what we perceive as reality isn't reality. As for the idea of a god existing, we do have plenty of reason to believe this is a false idea.
I may or may not get to the rest of the rest of the things you said. At least I have an answer, or at least a partial one, as to why you believe in God. It isn't because of faith but a misunderstanding or misinterpretation of science and/or potentially an assumption that God exists before searching for evidence.
There is a reason that you deny the existence of God and it has nothing to do with proof. I can show this to you. Examine what your initial reaction to the evidence of God's existence I offered already in this thread. Did you think that you could continue to deny God because you are not a scientist, or philosopher but 'Surely somewhere, sometime, a philosopher or scientist will come up with an explanation for universal, immaterial, unchanging laws apart from God?' Did you try to come up with an alternate explanation on your own? OR Did you even consider that the proof was valid? OR (as it seems that you have actually done) did you simply look over the evidence and ignore it to continue in your way of thinking? The last would be rejecting any rational way of thinking and deliberately continue in your misinformation which means that your lack of the knowledge of truth is your own fault for not truly seeking the truth.
I think you are confusing my assumption with my presupposition.
You assume there is no God therefore you block out all logic and reason as evidence.
The Laws of logic definitely exist despite whether or not a mind exists that can interpret them. It is not like the instantiation principle (if all red objects went out of existence, then red would cease to exist) as everything that exists is logical. So unless you are willing to say that nothing exists, then logic will always exist. They are what's known as absolute truth. This means that they are always true anywhere in the universe at any given time.
Since you don't seem to want to watch the video I posted (and it seems as though you are just taking any assumption other than the only logical answer (ie. God)), I will post two links to a text version of what TAG is.
Not the best:
The Transcendental Argument for the Existence of God | CARM.org
Much better and much shorter!:
Proof That God Exists.org
Let me define absolute truth.
The law of non-contradiction is an absolute truth. A statement that contradicts itself is not a true statement. For example, to say that a cloud is not a cloud is not a true statement.
Whether a mind exists that conceives this law is irrelevant. This law is true as gravity is true. I can deny gravity all I want but if I jump out of a 20-story building I'm going to fall and hit the ground.
Please visit the links above. They are all the proof any person really needs. Not only this, but if would actually show that since you are considering the existence of God, then you would actually be seeking the truth. To not look at arguments of the other side is proof that you are not willing to know the truth and you are only trying to suppress it just like the Bible says you would do in Romans 1 which gives more evidence since you would be proving Romans chapter one to be true.