I'm more than halfway through it but I've heard it all before. I don't accept his definitions. Axiomatic concepts can not be defined in terms of other concepts, they can only be defined ostensively and there is no warrant for dividing a fundamental concept the way he does. As I said, it's pure rationalism. By what means is he aware of this kind of being that is unlike everything else? Please answer this one question for me if nothing else. Is it some way other than imagining?
I can imagine the nothingness, the state of things before there was a Universe, or anything else, except God. But I can't imagine God. But imagination is irrelevant to being aware of God. There is the witness of the Spirit of God to the heart of those it inhabits, and the presence of God one begins to accept as such, which is (at least for me) kind of analogous to the presence of someone I live with, that I am not looking at or hearing speak, a presence I am not at most times thinking of but that is nevertheless there. There is also something else, that I don't know how to begin to describe. But the experience of God is not epistemic, in the sense that it is not useful in proving God's existence or person, (except, perhaps, to the one experiencing his presence etc.), in the way we consider most other things we see (for example, "I know I exist, because I experience awareness".)
Math and reason are used in science all the time. Logical sequence serves for epistemic evidence, though one may not even realize they are using it that way, to arrive at conclusions. Scientists would prefer to have epistemic evidence to prove the steps in their logic, and they would like to have experiments to observe what they theorize, but they can't always, and instead assume an "IF" to continue with their logical progression.
So it is with the rational proof of the existence of God. The cosmological argument works, and is elegantly simple. It is plenty of reason for me to say, that it makes more sense that God (being first cause, and I will accept no other) should exist, than that I exist, but here I am, so obviously, God is. But it would take longer than the many thousands, (or billions), of years to demonstrate experimentally, the many causal steps between First Cause, and the effect, Me.
I assume you are referring to "existence" as the "fundamental concept" that you see no warrant for Sproul to divide. I would say that 'existence' is a fundamental concept, but only as fundamental as any other principle that depends on First Cause for its meaning. If you say "existence is", I say, "existence is because First Cause is." and not the other way around. Existence, logic and reason, and even fact reality, itself, derive from First Cause. He is not subject to them as though they are fundamental principles into which he must fit, but they depend on him for their rule over other effects.
Of course, we use them in describing him; we say that he exists, and that what he does must fit logic, and that he is real, but we only mean by these whatever WE know them to be, and should not use them to say that he is subject to them. God is what he is, and does what he does, and all else proceeds from that, or he is not first cause.
And by the way, existence as existence is self-existent and logically could not be otherwise. It's important to define what existence means. The concept existence subsumes everything that exists including everything that has ever existed, exists now, and will ever exist. This is because time and place are measurements that are despecified, like all other measurements, in the forming of an abstraction. This is why a theory of concepts is crucial.
Nothing, not even existence, can cause itself. That is self-contradictory. Self-existence, a term we use to help us think, is at best a principle, and non-governing over effects (i.e. it doesn't cause anything), but only defining of other things, and not itself. But even as a fundamental principle, if indeed it is a fundamental principle, then, it is caused.
One can assert this about anything one imagines. Sparky does not answer to form, whatever that is supposed to mean. Sparky is an absolute, uncaused, self-existent, unchanging, necessary being that is a different kind of being from every other kind.
You said Sparky was a unicorn. Thus, he answers to the form we know as 'Unicorn'. God does not. All things derive what they ontologically are, from first cause, and not he from them.