For all my non-Catholic friends, the title should not suggest that we Catholics don't believe that Christ was God. We absolutely believe in His divinity. However, these questions treat God's knowledge in the Divine nature, and Christ's knowledge in human nature. It's a rather interesting exercise that St. Thomas puts us through.
A1. Possessing a human soul (a rational soul), Christ possessed created knowledge. A perfect human soul has potential to know intelligible things. To be perfect it must know what is intelligible. If Christ had had an intellect, it would have been to no purpose if He had not used it to know that which was intelligible. Created knowledge belongs to the human soul by nature. Since nothing was wanting in Christ, He did not want created knowledge.
A2. Man has the knowledge of the blessed in potentiality. Men are brought to this beatitude through Christ’s humanity. So this knowledge had to belong to Christ pre-eminently since cause must be more efficacious than the effect. Christ must have what He gives to others.
A3. Everything potentially is imperfect unless it is reduced to act. The passive intellect of man is potential until it is reduced to act in intelligible species, which are its completed form. The Word imprinted upon the soul of Christ all things that are potential in the human intellect. Christ knows the Word, and all things in the Word, and all things in their proper nature as they make sense to the human mind.
A4. Christ’s human nature lacked nothing that our nature has, so Christ had both a passive and an active intellect as we do, and it functioned in the same fashion in relation to objective experience and “intelligible species.” Thus, Christ acquired knowledge by the action of His active intellect.
A1. In the Incarnation, the Divine and human natures remain unconfused or intermingled. So the uncreated remained as it was, and the created was still limited by its nature. It’s impossible for a finite creature to comprehend the Divine Essence, which is infinite (that is, finite cannot comprehend the simply infinite).
A2. All things (to an extent) belong to Christ as the creator and judge, and any created intellect knows more perfectly in the Word what they knew before being beatified. All beatified intellects know whatever pertains to themselves. So the soul of Christ, being both beatified and being Christ, would know everything existing in time that the Word knows. Some things are in Divine power alone and cannot be known by the soul of Christ (for example, potentialities in God that are never actualized). However, anything potential in created being would have been known by the soul of Christ.
A3. Knowledge regards being, which is said either to be in act or in potential. Things are known primarily as they are in act rather than in potential, which is known secondarily by way of the one in whose power it could exist. In regard to the first, Christ cannot know the infinite because there are not an infinite number in act regardless of how many acts may take place since they are all temporally bound. In the second sense, Christ does know the infinite because He knows the power in the creature, which is infinite even though its acts are not.
A4. While the blessed see the Divine Essence, the soul of Christ is more closely joined to the Word than any other creature, so it receives the full illumination in which God is seen by the Word Himself, more so than any other creature. So more perfectly than all other creatures does the soul of Christ see the First Truth, which is the Essence of God.
A1. Intelligent beings have their own form but also the forms other things as ideas, a thing known in one who knows. Forms approach, in their immateriality, a kind of infinity. God possesses the highest degree of immateriality (I,7,1), so He occupies also the highest place of knowledge.
A2. God understands Himself through Himself. Some operations are internal in the operator, having the object of term within. When we know of an object within, we know that which is intelligible through our intellect in act. Each can be in potential, but the object is known by the intellect in operation or act. In God, there is no potential of intellect or object, and intellect and object are the same. The intelligible species in God is the Divine intellect. God does not have knowledge, but is knowledge.
A3. A thing is comprehended when the end of knowledge about it has been attained, that is, when it is known as perfectly as it can be known. God knows Himself perfectly, and He is knowable according to His own mode of actuality. The power of God in knowledge is as great as His actuality in existence, which is pure act and free from any potentiality. So He is supremely knowable and knows Himself supremely. Hence, He comprehends Himself.
A4. If God’s act of understanding were something different than His substance, then something other than His substance would be the act and perfection of His substance, which would mean that His substance was related as potentiality to the act of understanding, and this we know is not possible since He is pure act, and the act of understanding is the perfection of the one who understands. In addition, to understand is not something extrinsic to the one understanding but remains in the one understanding and is the perfection of the one understanding, just as existence is the perfection of the one who exists. Since God’s existence is His essence, His essence is also His intelligible species, so His act of understanding, His intellect, is the same as His essence and existence.
A5. God necessarily knows things other than Himself. He perfectly understands Himself. If He knows Himself perfectly, He knows His power perfectly. Since His power extends to other things as He is their First Cause, He necessarily knows things other than Himself. Otherwise He would not know the extent of His own power. So all things that pre-exist in God must be within His act of understanding. Yet as He sees Himself through Himself, He also sees other things not in themselves but in Himself.
A6. To know a thing in general and not in particular is to know it imperfectly. If God knows things only in general, His understanding would not be perfect. So God must have proper knowledge of this, both that which is general and common to all and that which distinguishes one from another. Any perfection that exists in any creature, pre-exists in God, hence, must be known in proper ratio.
A7. We know things discursively in two ways: successively and by causality. However, many things that we could understand in succession we can also understand simultaneously, as parts of a composite. God, however, sees all things in Himself, which is one thing, so He sees them immediately rather than sequentially. In the second case, one who proceeds from cause to effect moves from principles to conclusions rather than both at once, or from what is known to what is unknown. But God sees effects in Himself as the cause, so He does not see discursively.
A8. The knowledge of God to all things is likened to the knowledge of a craftsman to the things he makes. The knowledge of the latter is the cause of the things he makes since he works by his own intellect, so the form of intellect must be the principle of action (the cause). To an intelligible form in an intellect, though, must also be added the will of the craftsman. So likewise is God’s knowledge, when joined to His will, the cause of things.
A9. God knows all things in whatever way they exist. Some things that do not have actual existence can be in terms of being possible in God’s power. They can exist in thought or imagination. Anything that can be made, thought, or said by a creature are known by God, even though they have no other material existence. However, such things are known not by vision but by simple intelligence.
A10. To know a thing perfectly, one must know everything accidental to it. Some good things can be corrupted by evil accidentally. Thus God could not know good things perfectly unless He also knew evil things. A thing is knowable to the degree in which it exists. Since evil is a privation of good, God knows evil in that He knows what is good and what can be lacking in it.
A11. All perfections found in creatures pre-exist in God in a higher way. To know singular things is part of our perfection, so God must likewise know singular things since what is known to us must also be known to God. Although we might know abstractions and singular things separately, God knows them both by His simple intellect. As mentioned in Q14 A4, since God is the cause of all this by His knowledge and His knowledge extends as far as His causality extends, He extends not only to forms but to the matter in which they inhere and are individualized. Thus He knows singular things.
A12. God knows all that is actual but also all that is possible to Himself or created things. Thus He must also know infinite things. The knowledge of a knower is measured by the mode of the form, which is the principle of knowledge. Now when we know something by sense, we know only of the immediate individual. However, when we know its nature, we can know infinite individuals that participate in that nature. So in some ways, we know the infinite, not as distinct individuals but in the principles of that species. However, the Divine essence is a likeness of all things that are or can be, not merely in universals but also in proper ratio top each individual. Thus His knowledge extends to infinite things.
A13. God knows all things, not only actual things but also things possible to Him and creatures. Since some of these are future contingent to us, it follows that God knows future contingent things. A contingent thing can be considered in itself, in which case it is not future but exists now in act (that is, an image of what will be). It can also be considered contingent in its cause, and in this way it is a future thing. Since God knows causes and effects simultaneously, He knows the contingent cause of a contingent effect together. So He knows the contingent future thing, which is future in relation to its cause.
A14. It is in our power to form enunciations, and God knows of all things in His power or those of His creatures. It follows that He knows enunciable things. He knows them not in the same manner as human intellects do, as if division or composition existed in His intellect, but by understanding the essentials of each thing, as well as all that is accidental to them.
A15. God’s knowledge is His substance, which is immutable. Thus, His knowledge is immutable
A16. Knowledge can be called speculative in three ways: first, on the part of things that are known but are not operable by the knower (for example, man’s knowledge of natural or divine things); second, in the manner of knowing (for example, as one considers what is necessary for a composition in general); and thirdly, as one considers different ways that a thing could be made without actually making it. Of Himself, God has only speculative knowledge since He in Himself is not operable. Otherwise, He has both speculative and practical knowledge because He can consider both what He can make and does not, as well as those things which He can make and does. So if He knows something in itself, it is speculative knowledge. If He knows something that is directed toward an end, it is practical.