Sure, I'll add my thoughts regarding the distinction between the two...
Proposition One: Existence --- Existence must first be defined, since people can wander off onto a different path right from that very beginning point. What IS existence? Are we speaking of the type of existence, such as "my computer exists"? Or are we speaking of the type of existence, such as "Frodo Baggins exists"? The first example is an existence in objective reality, while the second example is an existence in lore. (books, movies, story, mythology, ...)
If we agree upon using the first type of existence (objective reality), then discussion can move into determining whether or not something exists in that particular way. DOES God exist in objective reality? First, God must be defined... I will get more into that in the 2nd part, but just assume that the definition of God is agreed upon. Then, we need to figure out how we know whether something exists in objective reality or not. Keep in mind that "reality" is differently experienced by each individual... Can we simply rely on our five senses? Obviously not, since things objectively exist that we can't sense with our five senses (without using instrumentation to 'enhance our senses', anyway). We seem to have issues sensing very small things and very large things (going 'beyond our scope' in either direction)... Does that mean that those things don't objectively exist? No... Does that mean that those things DO objectively exist? Still no...
This leads us into answering Proposition One (that God is.) Well, IS God?? Arguments can be made either way, depending on what evidence one accepts/rejects... So, does God objectively exist? We definitely know that there IS an absolutely truthful answer to the question, since it can be logically reasoned that absolute truth exists, and we know that the answer to that question has to be either 'yes' or 'no', but there is no way to prove or disprove God's existence, hence the options of theism, atheism, and agnosticism... To attempt to prove or disprove God's existence leads to logical fallacies, such as the circular argument fallacy and the argument from ignorance fallacy. In conclusion, Proposition One (that God is) can only be logically accepted or rejected on a faith basis.
Proposition Two: Nature --- Regardless of which definition of "existence" is believed with regards to God, one can discuss the nature of God, as this is NOT a discussion regarding the existence of God. This is more or less an attempt to define God, as I eluded to earlier. Now, how does one define God? First, we need to be talking about the same God... I will use the Christian God as my example. How does one define the Christian God? Well, Christians view The Bible as their holy scripture, so it would make sense for one to base the definition of God off of what The Bible says about God (in other words, to keep discussion about the nature of God within the framework of The Bible).
What IS the nature of God? How is God best defined? Well, God goes beyond our five senses, and any augmentation of our senses, IF he objectively exists, so we can't use any of our five senses to define him. Therefore, we can only go by what is said about him (ie, what his qualities are). I think he is best defined by his qualities. Using The Bible as a framework, we learn that God is omniscient, omnipresent, and omnipotent. We also learn that he is a timeless, spaceless, immaterial, intelligent, and personal being. I'd say that those qualities are the best way to define what the Christian God is (his nature).
