N.B. St. Thomas does not address all of these quotes directly or in their entirety.
St. Dionysius the Areopagite
Whether any created intellect can see the essence of God? (Yes)
On the Divine Names 1:4: the superessential Illimitability is placed above things essential, and the Unity above mind above the Minds; and the One above conception is inconceivable to all conceptions; and the Good above word is unutterable by word—Unit making one every unit, and superessential essence and mind inconceivable, and Word unutterable, speechlessness and inconception, and namelessness—being after the manner of no existing being, and Cause of being to all, but Itself not being, as beyond every essence…
ST I, q. 12, art. 1, ad 3: God is not said to be not existing as if He did not exist at all, but because He exists above all that exists; inasmuch as He is His own existence. Hence it does not follow that He cannot be known at all, but that He exceeds every kind of knowledge; which means that He is not comprehended.
On the Divine Names 1:5: It is superior to every expression and every knowledge, and is altogether placed above mind and essence,—being such as embraces and unites and comprehends and anticipates all things, but Itself is altogether incomprehensible to all, and of It, there is neither perception nor imagination, nor surmise, nor name, nor expression, nor contact, nor science…
ST I, q. 12, art. 1, ad 1: This authority “speak[s] of the vision of comprehension.”
Whether a name can be given to God? (Yes)
On the Divine Names 1:5: “the superessential Deity is shown to be without Name, and above Name.”
ST I, q. 13, art. 1, ad 1: “The reason why God has no name, or is said to be above being named, is because His essence is above all that we understand about God, and signify in word.”
Whether affirmative propositions can be formed about God? (Yes)
On the Heavenly Hierarchy 2:3: “the negations respecting things Divine are true, but the affirmations are inharmonious…”
ST I, q. 13, art. 2, ad 1: “Dionysius says that the affirmations about God are vague or, according to another translation, ‘incongruous,’ inasmuch as no name can be applied to God according to its mode of signification.”
Whether the human intellect can attain to the vision of God in His essence? (Yes)
Letter 1 to Gaius: His pre-eminent darkness is both concealed by every light, and is hidden from every knowledge. And, if any one, having seen God, understood what he saw, he did not see Him, but some of His creatures that are existing and known. But He Himself, highly established above mind, and above essence, by the very fact of His being wholly unknown, and not being, both is super-essentially, and is known above mind.
ST III-S, q. 92, art. 1, ad 4: God is light (John 1:9). Now illumination is the impression of light on an illuminated object. And since the Divine essence is of a different mode from any likeness thereof impressed on the intellect, he (Dionysius) says that the “Divine darkness is impervious to all illumination,” because, to wit, the Divine essence, which he calls “darkness” on account of its surpassing brightness, remains undemonstrated by the impression on our intellect, and consequently is “hidden from all knowledge.” Therefore if anyone in seeing God conceives something in his mind, this is not God but one of God’s effects.
Letter 5 to Dorotheus: The Divine gloom is the unapproachable light in which God is said to dwell. And in this gloom, invisible indeed, on account of the surpassing brightness, and unapproachable on account of the excess of the superessential stream of light, enters every one deemed worthy to know and to see God, by the very fact of neither seeing nor knowing, really entering in Him, Who is above vision and knowledge…
ST III-S, q. 92, art. 1, ad 5: “Although the glory of God surpasses any form by which our intellect is informed now, it does not surpass the Divine essence, which will be the form of our intellect in Heaven: and therefore although it is invisible now, it will be visible then.”
St. John of Damascus
Whether any name can be applied to God substantially? (Yes)
An Exact Exposition of the Orthodox Faith 1:9: Each then of the affirmations about God should be thought of as signifying not what He is in essence, but either something that it is impossible to make plain, or some relation to some of those things which are contrasts or some of those things that follow the nature, or an energy.
ST I, q. 13, art. 2, ad 1: “Damascene says that these names do not signify what God is, forasmuch as by none of these names is perfectly expressed what He is; but each one signifies Him in an imperfect manner, even as creatures represent Him imperfectly.”
Whether the name of Image is proper to the Son? (Yes)
An Exact Exposition of the Orthodox Faith 1:13: “The Son is the Father’s image, and the Spirit the Son’s, through which Christ dwelling in man makes him after His own image.”
ST I, q. 35, art. 2, ad 1: “Damascene and the other Greek Doctors commonly employ the term image as meaning a perfect similitude.”
Whether the Holy Ghost proceeds from the Son? (Yes)
An Exact Exposition of the Orthodox Faith 1:8 [PG 94:832B]: “And we do not speak of the Spirit as from the Son: but yet we call Him the Spirit of the Son.”
ST I, q. 36, art. 2, ad 3: The Nestorians were the first to introduce the error that the Holy Ghost did not proceed from the Son, as appears in a Nestorian creed condemned in the council of Ephesus. This error was embraced by Theodoric the Nestorian, and several others after him, among whom was also Damascene. Hence, in that point his opinion is not to be held. Although, too, it has been asserted by some that while Damascene did not confess that the Holy Ghost was from the Son, neither do those words of his express a denial thereof.