Again, the simplicity of the 1st level of God means that God is not composed of material parts that interact according to some law of nature that defines and conditions God. God is not a body, nor is composed of matter and form.
The simplicity of the 2nd-level God the Son I describe in (the admittedly flawed) Understanding the Blessed Trinity:
God's essence as a thinking being is manifested in God's having thoughts. What are the thoughts about? Himself. God comprehends Himself in a single self-image or self-conception.
But comprehending oneself which in this case is holding of one's image in one's mind is owning oneself which pertains to power. (God's power to create the world is due to His 3rd level of goodness.)
Further, since God's happiness lies not in anything outside God but rather within Himself (such that the Son suffices Himself), for God, again, love of concupiscence is the same as love of self. In keeping Himself in His mind, God ipso facto unites Himself and His understanding of Himself. But love is the only 2nd-level unitive force. Hence, God to His thought is as lover to the beloved. Insofar as God loves the thing He owns, He loves and enjoys Himself.
We see that the act of God's intellect, the act of His power, and act of His will are one and the same thing, namely, God's conceiving and contemplating Himself. Consequently, the distinction between the three faculties is illusory. God is one (and so is a simple pure act) and supremely so.
In addition, the Son is not a union of past, present, and future life but lives in eternity -- a simultaneously-whole and perfect possession of interminable life.
Further aspects of simplicity are described by St. Thomas in (ST, I, 3), where he argues that God is not composed of (1) essence and concrete object, (2) essence and existence, (3) genus and difference, or (4) subject and accident.
(1) The abstract essence known by the Father and the Son's suppositum are one.
(2) The procession of the Son from the Father is essential to God. It is the nature of the Father to beget the Son.
(3) The Son is not composed of any relevant property he shares with another thing + another property by which He is different from it.
Thus, "God is not related to creatures as though belonging to a different 'genus,' but as transcending every 'genus,' and as the principle of all 'genera'." (ST, I, 4, 3, reply 2)
(4) Every divine property is essential to God. If God is essentially omniscient, then He would cease to exist entirely, if omniscience were somehow taken away from Him. Conversely, if God ceased to exist, then omniscience could not be predicated of anything else.
It may be that all 4 of these dualities apply to all 3 levels, but not in the same way. For example, the Father's essence is His existence in one sense. The Son is also a union of essence and existence but for a different reason, viz., if these were separate in the Son, then they could be cleaved from each other, and so it would be possible to kill the Son. But this danger would interfere with His perfect happiness which is unfitting. Even the 1st level may feature the identity of essence and existence, lest it ceases to be pure act.