Binary Morality and other Religious Quandaries

So, I had a conversation the other day with one of my classmates about religion and the way we view morality; both of us are in a discrete math class and we came up with a few basic axioms of religion we figured were mutually exclusive (that is, only one can be true):

A) There is one and only one God
B) There are many gods
C) There is no god

Here we would likely define the "kami" of Shintoism and the boddhisatvas of Buddhism as a religion favoring the many gods axiom (as well as similar beliefs).

As much as everyone would like to be accepting or tolerant, this is kind of the way it is: By believing in any particular religion you are accepting the premise that people who don't believe the same way you do about one of the basic axioms are wrong.

Settling that, we started talking about pretty nebulous ideas like justice, mercy, and morality in general. We were mostly talking about Protestantism vs LDS beliefs (since my classmate is LDS and I'm a Protestant with LDS uncles, aunts, and cousins). In talking about the idea of justice, I put forth the idea that justice as we see it is entirely subjective; that is, we see a theft and we judge that a relatively short term of imprisonment is payment enough, but the rape and murder of a child deserves life imprisonment or capital punishment: death.

Now, again this is entirely subjective because, at least in my understanding of the Bible, God sees sin simply as a sin. It has neither a gradient nor is it cumulative. All of that comes down to a premise of mine about the way God looks at things. I think if we think of it in binary terms (1 is clean of sin, 0 is sinful), you can only attain '1' by either accepting Jesus as your savior, or by being Jewish and practicing the cleansing rituals. If we further pontificate on the verses about man being inherently imperfect and the flesh being naturally tempted toward sin, it stands to reason that '0' is the default state; and everyone under completely "fair and just" circumstances deserves to go to Hell (or whatever you wanna call your local burning pit of eternal torment). Me included.

Now when it comes to the idea of justice and mercy, my classmate was saying that you cannot receive mercy from the same entity/being as you would have received justice; that there has to be a third party for God to be "eternally unchanging." And here we went into a friendly debate about the nature of the Trinity (which is one of the main rift points between LDS and other Christians, a big enough point IMO to disinclude LDS as one of the sects of Christianity).

From my interpretation, the trinity is a set of 3 different manifestations of the same being. "The Father" is sort of the general-purpose manifestation that we envision ourselves praying to, that we think of as being on a golden throne in heaven, etc etc yada yada yada. "The Son" is Jesus, the savior, the messiah, the one we think of as lending the merciful hand (some people would even envision him as the defense attorney on our behalf before the Father in some place of ultimate judgement). Last is "The Holy Ghost/Spirit" which is how some envision the conscience, that which nudges us in the right direction when we come to a moral decision (though I think of my own conscience as something separate, and the Holy Ghost is more, God acting as the universal hint system). But anyway, all three manifestations are just our own vision or idea about how things are, like looking at a C++ or Java implementation when what's in Assembly (or even just binary machine language) tells a slightly different story. All 3 are really the same entity.

As for how my classmate interpreted it, it goes back to the argument about God (The Father) being unchanging and incapable of offering Justice and Mercy at the same time; thereby necessitating a third party in the form of Jesus Christ, who under this understanding must be seen as a separate entity than The Father.

Well, if I misunderstood any of that (classmate who may or may not read this) feel free to correct me; and I'd love to hear others' opinions on the matter in the comments.