Hi, Eric. Emer. Prof. Thomas E. Woods, Jr. explains in his audio recording entitled "No, You're Not a Dummy For Believing in God" (TomWoodsTV, YouTube, Oct. 27, 2014) that, using the Thomistic terminology, an essentially ordered series requires the First Cause to contain all actuality and no potentiality, i.e., for it to be pure actuality; or, in other words, for the First Cause to be all potentiality fully realized, i.e., fully actualized.
This by itself gives a rather detailed definition of God, since logically there are an infinite number of potentials which can be actualized, this requires the First Cause to be infinite action, i.e., that God is the collection of all action which is logically possible to take place, which includes all thoughts which are logically possible to think. Since the potential for such thoughts is logically infinite, we already have the concept that the First Cause must be infinite in intellect, i.e., that it is omniscient: having an infinite intelligence and knowing all that is logically possible to be known. We also have the concept of the First Cause being omnipotent, because it is the collection of all logically possible action, of which is infinite. Additionally, we have the concept of God being omnipresent, since as Emer. Prof. Woods explains in his aforecited audio lecture, a perfect copy of a thing is that thing. This is actually called the Law of Identity in the field of logic, which requires that A = A. Since God is the collection of all action, all actions are simply subsets of God. From the Law of Identity, we also get the concept of the Oneness of the First Cause, i.e., of monotheism, because to posit different Entity which had all these properties yet which is not in fact the Entity we had previously been discussing would be equivalent to saying that A != A.
For much more on these matters, Eric, including the answers to your other concerns, see my below article, which details physicist and mathematician Prof. Frank J. Tipler's Omega Point cosmology and the Feynman-DeWitt-Weinberg quantum gravity/Standard Model Theory of Everything (TOE) correctly describing and unifying all the forces in physics. The Omega Point cosmology demonstrates that the known laws of physics (viz., the Second Law of Thermodynamics, General Relativity, and Quantum Mechanics) require that the universe end in the Omega Point: the final cosmological singularity and state of infinite informational capacity having all the unique properties traditionally claimed for God, and of which is a different aspect of the Big Bang initial singularity, i.e., the first cause. The Omega Point cosmology has been published and extensively peer-reviewed in leading physics journals.
Additionally, in the below resource are six sections which contain very informative videos of Prof. Tipler explaining the Omega Point cosmology and the Feynman-DeWitt-Weinberg quantum gravity/Standard Model TOE. The seventh section therein contains an audio interview of Tipler. I also provide some helpful notes and commentary for some of these videos.