I can agree with most of what you write save this. There are certain hypostatic properties which are attached only to one person. The Father, for example is the only cause and He alone is autotheos.
I am not familiar with autotheos.
The key for me is understanding the difference between person and nature. The Trinity is three persons with one nature. God is infinite. The three divine persons are infinite in nature.
Your nature is what you are, not who you are. Your nature determines what you do.
Jesus has God nature and human nature. He is one person with two natures.
God is three persons with one nature.
Sorry if I am repeating myself. This is difficult.
Jesus Christ is Jesus Christ. That is who he is. The Father is not the Son. But the Father and Son share identical natures.
This is difficult for us, because we are made male and female. Two different beings come together and make a unique person. All of us share human nature, but we are different by nature, some tall or short, black or white, highly intelligent or dull, curly haired or bald, musically gifted or tone deaf. We all have characteristics that are different, or even lacking in others, because we are finite. This can not be so if your nature is infinite.
We say that He is infinite in all His perfections. He is truth. He is love. He is justice. He is life.
In all these He is infinite. It is helpful to our understanding to think about things one at a time, separately. We can not segregate God’s perfections. God is love and life at the same time. They can not exist without one another. So in any of His perfections we find all the others.
Since God is infinite in them and we are finite then we can never completely know God. There is always something more, or new to discover. Jesus says He knows the Father and the Father knows Him.
The three persons must have or contain all the divine perfections or qualities to be infinite (God).
There are two most fundamental activities that are proper to all spiritual beings, God, angels and men. They are knowing and loving. Before the Creator created anything, God eternally exists. Everything else has a beginning.
For all eternity God exists and does those two things. He knows and loves. He knows and loves Himself, who He is, not what He is.
The Father knows the Son. The Son knows the Father. The Father, Son and Holy Ghost are who God is. The perfections is what God is, His nature.
If any of the persons of the Holy Trinity had some quality the other lacked there would not be three infinite persons.
I do not know the thought about God the Father being the only cause. I know you could not say that He is the first cause. First presumes time. In time we have a before and after. In God eternal there can be no before or after.
So the Father does not love the Son and then the Son returns love to the Father. That is a before and after. They give themselves to themselves simultaneously. Theologians say there is no potency in God, that God is pure act. The Father does not give Himself to the Son over time, a little then a little more. He gives Himself entirely all at once holding nothing back.
The reason we are made acceptable to God is Jesus gives Himself to the Father with us. He ascended to heaven bodily, with His human nature, taking us with Him as an offering to the Father who accepts it. But having accepted or received it He now has it also.
But with us, we say, God loved us first.
So Jesus says He is the alpha and omega, the first and last, the beginning and the end. He is also everything in between. He is God, before all, after all, and above all.
If the three persons are infinite in nature, then logic says they must be identical in nature, or they are not all three God, because God is infinite being. If one lacked something the other had, then the former would not be God, because infiniity can not lack anything.
God can not change. Change presumes time, before and after. Also if God changed and added some quality He did not have before, then He was not infinite before.
All of this holds together except for one thing, mercy. We are the objects of divine mercy. We do not exist eternally. God became merciful. God changed. We can not say God had the potential for mercy. God has no potency. He is pure act, eternal act.
He changes us who are in time, but in order to do so He must change Himself. Mystery!
God has mercy on us, because He pities us. He pities us, because we are helpless. So He redeems us. In our helplessness God helps us. Helplessness and power are opposites. God is all powerful. We are helpless. Our helplessness had the power to change omnipotence. Mystery!