Are you asking if God is self-aware? The God of the Abrahamic religions is, but then he is a man-made image of God. And Men said unto themselves, "Come, let us make God in our image, that we may understand him and attribute our own insane motives to him." And verily they did so.
But the real God, the real creative and sustaining force of the universe? Well, I recognize two distinct types of intelligence, the intelligence of Man and the intelligence of the Seed. Men are born ignorant (tabula rasa) and constantly acquire knowledge through experience and logical analysis, but this means their initial wisdom is woefully lacking and since their knowledge is always increasing it must never be perfect and complete. To the contrary, the seed is formed with all the knowledge it needs to build a stem of grass, a rose bush, a tall sycamore tree. Its knowledge will not increase, but it will not need to. Its knowledge is complete and entirely adequate to the purpose of creation.
God's intelligence is seed intelligence, complete in its wisdom to the purpose of universal creation and sustenance. Is God self-aware? Well, I don't know. Is the seed self-aware? Is DNA self-aware?
And about God's gender... If the universe comes from God as the oak from the acorn, we would expect the creation to have the gender of its creator. Cosmology tells us that the universe began with an equivalence of matter and anti-matter but that in the collisions of the two forms of matter, anti-matter was nearly eliminated while regular matter dominated as it continues to do in our universe today. So God's gender appears to be material rather than anti-material. However, the only difference between matter and anti-matter is the opposition of their electrical charges (and maybe a few other oppositions of which I am not aware???). Now matter is matter and anti-matter is anti-matter only because the one is dominant and the other is rare. If anti-matter had dominated in our universe, we would call
it matter and call matter anti-matter. The designations are subjective.
So is our assignment of gender to deity. It too is subjective and really meaningless, except for what it says about us. And you don't need me to explain what that is.
Samm