Why is the universe intelligible? I.e., how did it acquire that property? How did man acquire the property of intelligence, which is the key to knowledge of the intelligible order of the universe?
Do you believe that logic is a spontaneous production of matter?
Logic is a construction of the mind which is used to determine and order truth and information into knowledge and then to understanding and creative acts. The mind is a physical machine which supports the functions of sentience and rationality. W/o that physical machinery, there can be no instance of mind and thus no instance of logic.
It is notable that the universe itself is logical. That is, it is completely consistent, otherwise one could find and observe instances of A≠A in reality.
"Why is the universe intelligible?"
Intelligibility is a property of things which have properties that enable observability and which are logically consistent. All instances of any physical object has properties which allow those objects to interact with other physical objects. That interaction is a sensing process. The universe is intelligible, because all forms of energy that exist in it have properties which determine the nature of interaction(the sense/relationship process) and are logically consistent.
"how did it acquire that property?"
Fundamental physical objects do not aquire their properties, or essence. Their properties/essence is inherent in every instance of the object as long as the object is an instance of that particular form. ie. a photon does not aquire it's properties.
"How did man acquire the property of intelligence, which is the key to knowledge of the intelligible order of the universe? " The intelligible order of the universe exists independently whether any instance of an intellignet being exists, or not. It is as given above. The properties of the forms of energy that exist in this universe are what allow and provide for the evolutionary process that results in mind/man.
Again, there is Epicurus principle, which says keep every theory consistent with the facts. The properties of the stuff that provides for intelligibility, also provides for sentient rational mind that would arise from. That's deterministic. Epicurus principle and the instance of a sentient rational mind provides for freedom of choice.